Feedback control for nonlinear evolutionary equations with applications

In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zeng, Biao [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence

Übergeordnetes Werk:	Enthalten in: Nonlinear analysis / Real world applications - Amsterdam [u.a.] : Elsevier Science, 2000, 66
Übergeordnetes Werk:	volume:66

DOI / URN:	10.1016/j.nonrwa.2022.103535

Katalog-ID:	ELV007557736

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520			\|a In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition.
650		4	\|a Nonlinear evolutionary equation
650		4	\|a Feedback control
650		4	\|a Weakly continuous operator
650		4	\|a Optimal control
650		4	\|a Existence
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publishDate	2022
allfields	10.1016/j.nonrwa.2022.103535 doi (DE-627)ELV007557736 (ELSEVIER)S1468-1218(22)00018-9 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Zeng, Biao verfasserin (orcid)0000-0002-6439-4278 aut Feedback control for nonlinear evolutionary equations with applications 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition. Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 66 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:66 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 66
spelling	10.1016/j.nonrwa.2022.103535 doi (DE-627)ELV007557736 (ELSEVIER)S1468-1218(22)00018-9 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Zeng, Biao verfasserin (orcid)0000-0002-6439-4278 aut Feedback control for nonlinear evolutionary equations with applications 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition. Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 66 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:66 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 66
allfields_unstemmed	10.1016/j.nonrwa.2022.103535 doi (DE-627)ELV007557736 (ELSEVIER)S1468-1218(22)00018-9 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Zeng, Biao verfasserin (orcid)0000-0002-6439-4278 aut Feedback control for nonlinear evolutionary equations with applications 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition. Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 66 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:66 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 66
allfieldsGer	10.1016/j.nonrwa.2022.103535 doi (DE-627)ELV007557736 (ELSEVIER)S1468-1218(22)00018-9 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Zeng, Biao verfasserin (orcid)0000-0002-6439-4278 aut Feedback control for nonlinear evolutionary equations with applications 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition. Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 66 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:66 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 66
allfieldsSound	10.1016/j.nonrwa.2022.103535 doi (DE-627)ELV007557736 (ELSEVIER)S1468-1218(22)00018-9 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Zeng, Biao verfasserin (orcid)0000-0002-6439-4278 aut Feedback control for nonlinear evolutionary equations with applications 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition. Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 66 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:66 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 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_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 66
language	English
source	Enthalten in Nonlinear analysis / Real world applications 66 volume:66
sourceStr	Enthalten in Nonlinear analysis / Real world applications 66 volume:66
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bklname	Globale Analysis Funktionalanalysis
institution	findex.gbv.de
topic_facet	Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence
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container_title	Nonlinear analysis / Real world applications
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author	Zeng, Biao
spellingShingle	Zeng, Biao ddc 510 bkl 31.55 bkl 31.46 misc Nonlinear evolutionary equation misc Feedback control misc Weakly continuous operator misc Optimal control misc Existence Feedback control for nonlinear evolutionary equations with applications
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topic_title	510 DE-600 31.55 bkl 31.46 bkl Feedback control for nonlinear evolutionary equations with applications Nonlinear evolutionary equation Feedback control Weakly continuous operator Optimal control Existence
topic	ddc 510 bkl 31.55 bkl 31.46 misc Nonlinear evolutionary equation misc Feedback control misc Weakly continuous operator misc Optimal control misc Existence
topic_unstemmed	ddc 510 bkl 31.55 bkl 31.46 misc Nonlinear evolutionary equation misc Feedback control misc Weakly continuous operator misc Optimal control misc Existence
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title	Feedback control for nonlinear evolutionary equations with applications
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title_full	Feedback control for nonlinear evolutionary equations with applications
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title_sort	feedback control for nonlinear evolutionary equations with applications
title_auth	Feedback control for nonlinear evolutionary equations with applications
abstract	In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition.
abstractGer	In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition.
abstract_unstemmed	In the paper we are concerned with the feedback control system governed by nonlinear evolutionary equations involving weakly continuous operators. By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. Moreover, we apply the main results to a class of differential variational inequalities, evolutionary hemivariational inequalities and the non-stationary Navier–Stokes–Voigt equation with a subgradient inclusion condition.
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title_short	Feedback control for nonlinear evolutionary equations with applications
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up_date	2024-07-06T16:40:40.358Z
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By using the Rothe method and a surjectivity result for weakly continuous operators, we first present the solvability for the evolutionary equation. Then we show the existence of solutions to the feedback control system. We also consider an existence result for an optimal control problem. 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Feedback control for nonlinear evolutionary equations with applications

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