Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations (Memoirs of the American Mathematical Society)

Fragnelli, Genni/ Mugnai, Dimitri

American Mathematical Society（2016/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 83 p.
• 言語 ENG
• 商品コード 9781470419547
• DDC分類 515.3534

Full Description

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.

Contents

Chapter 1. Introduction
Chapter 2. Mathematical tools and preliminary results
Chapter 3. Carleman estimate for non degenerate parabolic problems with non smooth coefficient
Chapter 4. Carleman estimate for degenerate non smooth parabolic problems
Chapter 5. Observability inequalities and application to null controllability
Chapter 6. Linear and Semilinear Extensions
Chapter 7. Final Comments
Appendix A. Rigorous derivation of Lemma 3.5