Existence of Solutions for Degenerate Parabolic Equations with Singular Terms
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Published: 2016
Total Pages:
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DOWNLOAD EBOOKRead and Download eBook Full
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Published: 2016
Total Pages:
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DOWNLOAD EBOOKAuthor: Emmanuele DiBenedetto
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 402
ISBN-13: 1461208955
DOWNLOAD EBOOKEvolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Author: Oscar Valverde Ayala
Publisher:
Published: 1975
Total Pages: 54
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DOWNLOAD EBOOKAuthor: Genni Fragnelli
Publisher: Springer Nature
Published: 2021-04-06
Total Pages: 105
ISBN-13: 303069349X
DOWNLOAD EBOOKThis 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: Chaohao Gu
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 193
ISBN-13: 9401111987
DOWNLOAD EBOOKIn the past few years there has been a fruitful exchange of expertise on the subject of partial differential equations (PDEs) between mathematicians from the People's Republic of China and the rest of the world. The goal of this collection of papers is to summarize and introduce the historical progress of the development of PDEs in China from the 1950s to the 1980s. The results presented here were mainly published before the 1980s, but, having been printed in the Chinese language, have not reached the wider audience they deserve. Topics covered include, among others, nonlinear hyperbolic equations, nonlinear elliptic equations, nonlinear parabolic equations, mixed equations, free boundary problems, minimal surfaces in Riemannian manifolds, microlocal analysis and solitons. For mathematicians and physicists interested in the historical development of PDEs in the People's Republic of China.
Author: Martial Marie-Paul Agueh
Publisher:
Published: 2002
Total Pages: 242
ISBN-13:
DOWNLOAD EBOOKAuthor: Paul Sacks
Publisher:
Published: 1981
Total Pages: 206
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DOWNLOAD EBOOKAuthor: Alexander A. Kovalevsky
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2016-03-21
Total Pages: 448
ISBN-13: 3110332248
DOWNLOAD EBOOKThis monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Author: Claude Le Bris
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2019-06-17
Total Pages: 156
ISBN-13: 311063550X
DOWNLOAD EBOOKThis book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
Author: J. Ildefonso Diaz
Publisher:
Published: 1983
Total Pages: 45
ISBN-13:
DOWNLOAD EBOOKDuring the last two decades a great deal of progress has been made on the mathematical analysis of flows through porous media. Such phenomena led to degenerate nonlinear parabolic equations. The equations obtained are of different nature when the fluid movement takes place in a horizontal column of the medium rather than in a vertical column of the medium. The latter case gives rise to first order nonlinear perturbations of the former case and equations of this more general sort also model the evaporation of a fluid through a porous medium. A significant technical difficulty arises in the evaporation case; the first order nonlinear terms can be singular at the points where the solution vanishes. In this paper the authors give a mathematical treatment of the Cauchy problem as well as the first and mixed boundary value problems for the relevant equations. Existence, continuity and uniqueness of generalized solutions are proved thereby improving earlier results in the mathematical literature.