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Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society SeriesPublisher: Providence : American Mathematical Society, 2016Copyright date: ©2016Edition: 1st edDescription: 1 online resource (96 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470429461
Subject(s): Genre/Form: Additional physical formats: Print version:: Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic EquationsDDC classification:
  • 515/.3534
LOC classification:
  • QA295 .F835 2016
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Mathematical tools and preliminary results -- 2.1. Well-posedness in the divergence case -- 2.2. Well-posedness in the non divergence case -- Chapter 3. Carleman estimate for non degenerate parabolic problems with non smooth coefficient -- 3.1. Preliminaries -- 3.2. The divergence case. -- 3.3. The non divergence case -- Chapter 4. Carleman estimate for degenerate non smooth parabolic problems -- 4.1. Carleman estimate for the problem in divergence form -- 4.2. Carleman estimate for the problem in non divergence form -- Chapter 5. Observability inequalities and application to null controllability -- 5.1. The divergence case -- 5.2. The non divergence case -- Chapter 6. Linear and Semilinear Extensions -- Chapter 7. Final Comments -- Appendix A. Rigorous derivation of Lemma 3.5 -- Acknowledgement -- Bibliography -- Back Cover.
Summary: The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. 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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Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Mathematical tools and preliminary results -- 2.1. Well-posedness in the divergence case -- 2.2. Well-posedness in the non divergence case -- Chapter 3. Carleman estimate for non degenerate parabolic problems with non smooth coefficient -- 3.1. Preliminaries -- 3.2. The divergence case. -- 3.3. The non divergence case -- Chapter 4. Carleman estimate for degenerate non smooth parabolic problems -- 4.1. Carleman estimate for the problem in divergence form -- 4.2. Carleman estimate for the problem in non divergence form -- Chapter 5. Observability inequalities and application to null controllability -- 5.1. The divergence case -- 5.2. The non divergence case -- Chapter 6. Linear and Semilinear Extensions -- Chapter 7. Final Comments -- Appendix A. Rigorous derivation of Lemma 3.5 -- Acknowledgement -- Bibliography -- Back Cover.

The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. 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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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