| eBook ISBN: | 978-1-4704-2946-1 |
| Product Code: | MEMO/242/1146.E |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $43.80 |
| eBook ISBN: | 978-1-4704-2946-1 |
| Product Code: | MEMO/242/1146.E |
| List Price: | $73.00 |
| MAA Member Price: | $65.70 |
| AMS Member Price: | $43.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 242; 2016; 83 pp
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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Table of Contents
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Chapters
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1. Introduction
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2. Mathematical tools and preliminary results
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3. Carleman estimate for non degenerate parabolic problems with non smooth coefficient
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4. Carleman estimate for degenerate non smooth parabolic problems
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5. Observability inequalities and application to null controllability
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6. Linear and Semilinear Extensions
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7. Final Comments
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A. Rigorous derivation of Lemma 3.5
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Additional Material
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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.
-
Chapters
-
1. Introduction
-
2. Mathematical tools and preliminary results
-
3. Carleman estimate for non degenerate parabolic problems with non smooth coefficient
-
4. Carleman estimate for degenerate non smooth parabolic problems
-
5. Observability inequalities and application to null controllability
-
6. Linear and Semilinear Extensions
-
7. Final Comments
-
A. Rigorous derivation of Lemma 3.5
