Carleman estimates, observability inequalities, and null controllability for interior degenerate nonsmooth parabolic equations / Genni Fragnelli, Dimitri Mugnai

Auteur: Fragnelli, Genni (1975-) - AuteurCo-auteur: Mugnai, Dimitri (1972-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 1146Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 2016Description: 1 vol. (V-84 p.) ; 26 cm ISBN: 9781470419547 ; br. ISSN: 0065-9266Résumé: Summary: We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are twofold. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence..Bibliographie: Bibliogr. p. 81-84. Sujets MSC: 35K65 Partial differential equations -- Parabolic equations and systems -- Degenerate parabolic equations
93B05 Systems theory; control -- Controllability, observability, and system structure -- Controllability
93B07 Systems theory; control -- Controllability, observability, and system structure -- Observability
93C30 Systems theory; control -- Control systems -- Systems governed by functional relations other than differential equations (such as hybrid and switching systems)
35Q93 Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with control and optimization
En-ligne: zbMath | MSN | AMS-résumé
Location Call Number Status Date Due
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Bibliogr. p. 81-84

Summary: We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are twofold. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

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