Carleman Estimates Observability Inequalities And Null Controllability For Interior Degenerate Nonsmooth Parabolic Equations PDF Download
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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 | : 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 | : 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 | : 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 | : 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 | : 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.
Author | : Shai M. J. Haran |
Publisher | : American Mathematical Soc. |
Total Pages | : 216 |
Release | : 2017-02-20 |
Genre | : Mathematics |
ISBN | : 147042312X |
Download New Foundations for Geometry: Two Non-Additive Languages for Arithmetical Geometry Book in PDF, ePub and Kindle
To view the abstract go to http://www.ams.org/books/memo/1166.
Author | : J. P. Pridham |
Publisher | : American Mathematical Soc. |
Total Pages | : 190 |
Release | : 2016-09-06 |
Genre | : Mathematics |
ISBN | : 1470419815 |
Download Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting Book in PDF, ePub and Kindle
The author defines and constructs mixed Hodge structures on real schematic homotopy types of complex quasi-projective varieties, giving mixed Hodge structures on their homotopy groups and pro-algebraic fundamental groups. The author also shows that these split on tensoring with the ring R[x] equipped with the Hodge filtration given by powers of (x−i), giving new results even for simply connected varieties. The mixed Hodge structures can thus be recovered from the Gysin spectral sequence of cohomology groups of local systems, together with the monodromy action at the Archimedean place. As the basepoint varies, these structures all become real variations of mixed Hodge structure.
Author | : Ariel Barton: |
Publisher | : American Mathematical Soc. |
Total Pages | : 122 |
Release | : 2016-09-06 |
Genre | : Mathematics |
ISBN | : 1470419890 |
Download Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces Book in PDF, ePub and Kindle
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.
Author | : Hans Lundmark |
Publisher | : American Mathematical Soc. |
Total Pages | : 102 |
Release | : 2016-10-05 |
Genre | : Mathematics |
ISBN | : 1470420260 |
Download An Inverse Spectral Problem Related to the Geng-Xue Two-Component Peakon Equation Book in PDF, ePub and Kindle
The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a "discrete cubic string" type, but presents some interesting novel features.