Carleman Estimates Observability Inequalities And Null Controllability For Interior Degenerate Nonsmooth Parabolic Equations PDF Download
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Author | : Genni Fragnelli |
Publisher | : |
Total Pages | : 84 |
Release | : 2016 |
Genre | : Carleman theorem |
ISBN | : 9781470429461 |
Download Carleman Estimates, Observability Inequalities, and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations Book in PDF, ePub and Kindle
We consider a parabolic problem with degeneracy in the interior of the spatial domain, and we 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.
Author | : Genni Fragnelli |
Publisher | : Springer |
Total Pages | : 105 |
Release | : 2021-04-07 |
Genre | : Mathematics |
ISBN | : 9783030693480 |
Download Control of Degenerate and Singular Parabolic Equations Book 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.
Author | : Genni Fragnelli |
Publisher | : American Mathematical Society |
Total Pages | : 19 |
Release | : 2021-11-16 |
Genre | : Mathematics |
ISBN | : 1470447878 |
Download Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences Book in PDF, ePub and Kindle
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Author | : Genni Fragnelli |
Publisher | : American Mathematical Soc. |
Total Pages | : 96 |
Release | : 2016-06-21 |
Genre | : Mathematics |
ISBN | : 1470419548 |
Download Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations Book 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.
Author | : P. Cannarsa |
Publisher | : American Mathematical Soc. |
Total Pages | : 225 |
Release | : 2016-01-25 |
Genre | : Mathematics |
ISBN | : 1470414961 |
Download Global Carleman Estimates for Degenerate Parabolic Operators with Applications Book 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.
Author | : Genni Fragnelli |
Publisher | : Springer Nature |
Total Pages | : 105 |
Release | : 2021-04-06 |
Genre | : Mathematics |
ISBN | : 303069349X |
Download Control of Degenerate and Singular Parabolic Equations Book 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.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : |
Download Local Null Controllability for Degenerate Parabolic Equations with Nonlocal Term Book in PDF, ePub and Kindle
Author | : Xiaoyu Fu |
Publisher | : Springer Nature |
Total Pages | : 127 |
Release | : 2019-10-31 |
Genre | : Mathematics |
ISBN | : 3030295303 |
Download Carleman Estimates for Second Order Partial Differential Operators and Applications Book 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.
Author | : |
Publisher | : |
Total Pages | : 294 |
Release | : 2011-11-01 |
Genre | : |
ISBN | : 9781461415855 |
Download Harnack's Inequality for Degenerate and Singular Parabolic Equations Book in PDF, ePub and Kindle
Author | : Steve Hofmann |
Publisher | : American Mathematical Soc. |
Total Pages | : 120 |
Release | : 2017-01-18 |
Genre | : Mathematics |
ISBN | : 1470422603 |
Download $L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets Book in PDF, ePub and Kindle
The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.