Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach

Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the p...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Colle, Blaise [verfasserIn] Lohéac, Jérôme Takahashi, Takéo

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Control Flatness Cross diffusion Free boundary

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Acta applicandae mathematicae - [S.l.] : Proquest, 1983, 187(2023), 1 vom: 29. Sept.
Übergeordnetes Werk:	volume:187 ; year:2023 ; number:1 ; day:29 ; month:09

Links:	Volltext

DOI / URN:	10.1007/s10440-023-00607-0

Katalog-ID:	SPR053246853

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520			\|a Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations.
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912			\|a GBV_ILN_213
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allfields	10.1007/s10440-023-00607-0 doi (DE-627)SPR053246853 (SPR)s10440-023-00607-0-e DE-627 ger DE-627 rakwb eng Colle, Blaise verfasserin aut Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. Control (dpeaa)DE-He213 Flatness (dpeaa)DE-He213 Cross diffusion (dpeaa)DE-He213 Free boundary (dpeaa)DE-He213 Lohéac, Jérôme (orcid)0000-0002-2785-268X aut Takahashi, Takéo (orcid)0000-0003-1270-6150 aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 187(2023), 1 vom: 29. Sept. (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:187 year:2023 number:1 day:29 month:09 https://dx.doi.org/10.1007/s10440-023-00607-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 187 2023 1 29 09
spelling	10.1007/s10440-023-00607-0 doi (DE-627)SPR053246853 (SPR)s10440-023-00607-0-e DE-627 ger DE-627 rakwb eng Colle, Blaise verfasserin aut Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. Control (dpeaa)DE-He213 Flatness (dpeaa)DE-He213 Cross diffusion (dpeaa)DE-He213 Free boundary (dpeaa)DE-He213 Lohéac, Jérôme (orcid)0000-0002-2785-268X aut Takahashi, Takéo (orcid)0000-0003-1270-6150 aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 187(2023), 1 vom: 29. Sept. (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:187 year:2023 number:1 day:29 month:09 https://dx.doi.org/10.1007/s10440-023-00607-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 187 2023 1 29 09
allfields_unstemmed	10.1007/s10440-023-00607-0 doi (DE-627)SPR053246853 (SPR)s10440-023-00607-0-e DE-627 ger DE-627 rakwb eng Colle, Blaise verfasserin aut Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. Control (dpeaa)DE-He213 Flatness (dpeaa)DE-He213 Cross diffusion (dpeaa)DE-He213 Free boundary (dpeaa)DE-He213 Lohéac, Jérôme (orcid)0000-0002-2785-268X aut Takahashi, Takéo (orcid)0000-0003-1270-6150 aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 187(2023), 1 vom: 29. Sept. (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:187 year:2023 number:1 day:29 month:09 https://dx.doi.org/10.1007/s10440-023-00607-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 187 2023 1 29 09
allfieldsGer	10.1007/s10440-023-00607-0 doi (DE-627)SPR053246853 (SPR)s10440-023-00607-0-e DE-627 ger DE-627 rakwb eng Colle, Blaise verfasserin aut Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. Control (dpeaa)DE-He213 Flatness (dpeaa)DE-He213 Cross diffusion (dpeaa)DE-He213 Free boundary (dpeaa)DE-He213 Lohéac, Jérôme (orcid)0000-0002-2785-268X aut Takahashi, Takéo (orcid)0000-0003-1270-6150 aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 187(2023), 1 vom: 29. Sept. (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:187 year:2023 number:1 day:29 month:09 https://dx.doi.org/10.1007/s10440-023-00607-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 187 2023 1 29 09
allfieldsSound	10.1007/s10440-023-00607-0 doi (DE-627)SPR053246853 (SPR)s10440-023-00607-0-e DE-627 ger DE-627 rakwb eng Colle, Blaise verfasserin aut Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. Control (dpeaa)DE-He213 Flatness (dpeaa)DE-He213 Cross diffusion (dpeaa)DE-He213 Free boundary (dpeaa)DE-He213 Lohéac, Jérôme (orcid)0000-0002-2785-268X aut Takahashi, Takéo (orcid)0000-0003-1270-6150 aut Enthalten in Acta applicandae mathematicae [S.l.] : Proquest, 1983 187(2023), 1 vom: 29. Sept. (DE-627)271176105 (DE-600)1479016-6 1572-9036 nnns volume:187 year:2023 number:1 day:29 month:09 https://dx.doi.org/10.1007/s10440-023-00607-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 187 2023 1 29 09
language	English
source	Enthalten in Acta applicandae mathematicae 187(2023), 1 vom: 29. Sept. volume:187 year:2023 number:1 day:29 month:09
sourceStr	Enthalten in Acta applicandae mathematicae 187(2023), 1 vom: 29. Sept. volume:187 year:2023 number:1 day:29 month:09
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Control Flatness Cross diffusion Free boundary
isfreeaccess_bool	false
container_title	Acta applicandae mathematicae
authorswithroles_txt_mv	Colle, Blaise @@aut@@ Lohéac, Jérôme @@aut@@ Takahashi, Takéo @@aut@@
publishDateDaySort_date	2023-09-29T00:00:00Z
hierarchy_top_id	271176105
id	SPR053246853
language_de	englisch
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author	Colle, Blaise
spellingShingle	Colle, Blaise misc Control misc Flatness misc Cross diffusion misc Free boundary Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach
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topic_title	Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach Control (dpeaa)DE-He213 Flatness (dpeaa)DE-He213 Cross diffusion (dpeaa)DE-He213 Free boundary (dpeaa)DE-He213
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title	Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach
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title_full	Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach
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title_sort	controllability results for a cross diffusion system with a free boundary by a flatness approach
title_auth	Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach
abstract	Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract We study a one-dimensional cross diffusion system with a free boundary modeling the Physical Vapor Deposition. Using the flatness approach, we show several results of boundary controllability for this system in spaces of Gevrey class functions. One of the main difficulties consists in the physical constraints on the state and on the control. More precisely, the state corresponds to volume fractions of the $n+1$ chemical species and to the thickness of the film produced in the process, whereas the controls are the fluxes of the chemical species. We obtain the local controllability in the case where we apply $n+1$ nonnegative controls and a controllability result for large time in the case where we apply $n$ controls without any sign constraints. We also show in this last case that the controllability may fail for small times. We illustrate these results with some numerical simulations. © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach
url	https://dx.doi.org/10.1007/s10440-023-00607-0
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author2	Lohéac, Jérôme Takahashi, Takéo
author2Str	Lohéac, Jérôme Takahashi, Takéo
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doi_str	10.1007/s10440-023-00607-0
up_date	2024-07-03T18:08:04.130Z
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score	7.4002924

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Controllability Results for a Cross Diffusion System with a Free Boundary by a Flatness Approach

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