Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms

Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is global...
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Autor*in:	Fernández, L. A. [verfasserIn] Zuazua, E.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1999

Systematik:	SA 6420 SA 6420

Anmerkung:	© Plenum Publishing Corporation 1999

Übergeordnetes Werk:	Enthalten in: Journal of optimization theory and applications - Kluwer Academic Publishers-Plenum Publishers, 1967, 101(1999), 2 vom: Mai, Seite 307-328
Übergeordnetes Werk:	volume:101 ; year:1999 ; number:2 ; month:05 ; pages:307-328

Links:	Volltext

DOI / URN:	10.1023/A:1021737526541

Katalog-ID:	OLC2026473196

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allfields	10.1023/A:1021737526541 doi (DE-627)OLC2026473196 (DE-He213)A:1021737526541-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Fernández, L. A. verfasserin aut Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1999 Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. Zuazua, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 101(1999), 2 vom: Mai, Seite 307-328 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:101 year:1999 number:2 month:05 pages:307-328 https://doi.org/10.1023/A:1021737526541 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 101 1999 2 05 307-328
spelling	10.1023/A:1021737526541 doi (DE-627)OLC2026473196 (DE-He213)A:1021737526541-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Fernández, L. A. verfasserin aut Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1999 Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. Zuazua, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 101(1999), 2 vom: Mai, Seite 307-328 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:101 year:1999 number:2 month:05 pages:307-328 https://doi.org/10.1023/A:1021737526541 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 101 1999 2 05 307-328
allfields_unstemmed	10.1023/A:1021737526541 doi (DE-627)OLC2026473196 (DE-He213)A:1021737526541-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Fernández, L. A. verfasserin aut Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1999 Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. Zuazua, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 101(1999), 2 vom: Mai, Seite 307-328 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:101 year:1999 number:2 month:05 pages:307-328 https://doi.org/10.1023/A:1021737526541 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 101 1999 2 05 307-328
allfieldsGer	10.1023/A:1021737526541 doi (DE-627)OLC2026473196 (DE-He213)A:1021737526541-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Fernández, L. A. verfasserin aut Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1999 Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. Zuazua, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 101(1999), 2 vom: Mai, Seite 307-328 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:101 year:1999 number:2 month:05 pages:307-328 https://doi.org/10.1023/A:1021737526541 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 101 1999 2 05 307-328
allfieldsSound	10.1023/A:1021737526541 doi (DE-627)OLC2026473196 (DE-He213)A:1021737526541-p DE-627 ger DE-627 rakwb eng 330 510 000 VZ 17,1 ssgn SA 6420 VZ rvk SA 6420 VZ rvk Fernández, L. A. verfasserin aut Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1999 Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. Zuazua, E. aut Enthalten in Journal of optimization theory and applications Kluwer Academic Publishers-Plenum Publishers, 1967 101(1999), 2 vom: Mai, Seite 307-328 (DE-627)129973467 (DE-600)410689-1 (DE-576)015536602 0022-3239 nnns volume:101 year:1999 number:2 month:05 pages:307-328 https://doi.org/10.1023/A:1021737526541 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2014 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4193 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 SA 6420 SA 6420 AR 101 1999 2 05 307-328
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title	Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms
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title_full	Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms
author_sort	Fernández, L. A.
journal	Journal of optimization theory and applications
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author_browse	Fernández, L. A. Zuazua, E.
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author-letter	Fernández, L. A.
doi_str_mv	10.1023/A:1021737526541
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title_sort	approximate controllability for the semilinear heat equation involving gradient terms
title_auth	Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms
abstract	Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. © Plenum Publishing Corporation 1999
abstractGer	Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. © Plenum Publishing Corporation 1999
abstract_unstemmed	Abstract This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient ∇y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, ∇y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces. © Plenum Publishing Corporation 1999
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title_short	Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms
url	https://doi.org/10.1023/A:1021737526541
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up_date	2024-07-04T04:03:00.939Z
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