Global Carleman Estimates for Degenerate Parabolic Operators with Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Carleman Estimates for Degenerate Parabolic Operators with Applications write by P. Cannarsa. This book was released on 2016-01-25. Global Carleman Estimates for Degenerate Parabolic Operators with Applications available in PDF, EPUB and Kindle. Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.
Carleman Estimates for Second Order Partial Differential Operators and Applications
Carleman Estimates for Second Order Partial Differential Operators and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Carleman Estimates for Second Order Partial Differential Operators and Applications write by Xiaoyu Fu. This book was released on 2019-10-31. Carleman Estimates for Second Order Partial Differential Operators and Applications available in PDF, EPUB and Kindle. This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations
Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations write by Genni Fragnelli. This book was released on 2016-06-21. Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations available in PDF, EPUB and Kindle. 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.
Control of Degenerate and Singular Parabolic Equations
Control of Degenerate and Singular Parabolic Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Control of Degenerate and Singular Parabolic Equations write by Genni Fragnelli. This book was released on 2021-04-06. Control of Degenerate and Singular Parabolic Equations available in PDF, EPUB and Kindle. This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I
Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I write by Jérôme Le Rousseau. This book was released on 2022-03-28. Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I available in PDF, EPUB and Kindle. This monograph explores applications of Carleman estimates in the study of stabilization and controllability properties of partial differential equations, including the stabilization property of the damped wave equation and the null-controllability of the heat equation. All analysis is performed in the case of open sets in the Euclidean space; a second volume will extend this treatment to Riemannian manifolds. The first three chapters illustrate the derivation of Carleman estimates using pseudo-differential calculus with a large parameter. Continuation issues are then addressed, followed by a proof of the logarithmic stabilization of the damped wave equation by means of two alternative proofs of the resolvent estimate for the generator of a damped wave semigroup. The authors then discuss null-controllability of the heat equation, its equivalence with observability, and how the spectral inequality allows one to either construct a control function or prove the observability inequality. The final part of the book is devoted to the exposition of some necessary background material: the theory of distributions, invariance under change of variables, elliptic operators with Dirichlet data and associated semigroup, and some elements from functional analysis and semigroup theory.
