Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations.
Material type:
- text
- computer
- online resource
- 9781470429461
- 515/.3534
- QA295 .F835 2016
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.
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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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