Linear And Quasilinear Parabolic Problems
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Linear And Quasilinear Parabolic Problems
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Author : Herbert Amann
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Linear And Quasilinear Parabolic Problems written by Herbert Amann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Differential equations, Parabolic categories.
Linear And Quasilinear Parabolic Problems
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Author : Herbert Amann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Linear And Quasilinear Parabolic Problems written by Herbert Amann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this treatise we present the semigroup approach to quasilinear evolution equa of parabolic type that has been developed over the last ten years, approxi tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.
Parabolic Quasilinear Equations Minimizing Linear Growth Functionals
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Author : Fuensanta Andreu-Vaillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-26
Parabolic Quasilinear Equations Minimizing Linear Growth Functionals written by Fuensanta Andreu-Vaillo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-26 with Computers categories.
This book details the mathematical developments in total variation based image restauration. From the reviews: "This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters....The book is written with great care, paying also a lot of attention to the bibliographical and historical notes."-- ZENTRALBLATT MATH
Linear And Quasilinear Parabolic Problems
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Author : Herbert Amann
language : en
Publisher: Springer
Release Date : 2019-04-16
Linear And Quasilinear Parabolic Problems written by Herbert Amann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-16 with Mathematics categories.
This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.
Linear And Quasi Linear Equations Of Parabolic Type
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Author : Olʹga Aleksandrovna Ladyzhenskai͡a
language : en
Publisher: American Mathematical Soc.
Release Date : 1968
Linear And Quasi Linear Equations Of Parabolic Type written by Olʹga Aleksandrovna Ladyzhenskai͡a and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Moving Interfaces And Quasilinear Parabolic Evolution Equations
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Author : Jan Prüss
language : en
Publisher: Birkhäuser
Release Date : 2016-07-25
Moving Interfaces And Quasilinear Parabolic Evolution Equations written by Jan Prüss and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
Fractional In Time Semilinear Parabolic Equations And Applications
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Author : Ciprian G. Gal
language : en
Publisher: Springer Nature
Release Date : 2020-09-23
Fractional In Time Semilinear Parabolic Equations And Applications written by Ciprian G. Gal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Mathematics categories.
This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics. Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions. This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.
Elliptic And Parabolic Equations With Discontinuous Coefficients
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Author : Antonino Maugeri
language : en
Publisher: Wiley-VCH
Release Date : 2000-12-13
Elliptic And Parabolic Equations With Discontinuous Coefficients written by Antonino Maugeri and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-13 with Mathematics categories.
This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.
Linear And Quasilinear Parabolic Problems
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Author : Herbert Amann (Mathematiker, Deutschland, Schweiz)
language : en
Publisher:
Release Date : 1995
Linear And Quasilinear Parabolic Problems written by Herbert Amann (Mathematiker, Deutschland, Schweiz) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Recent Advances In Nonlinear Analysis
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Author : Michel Chipot
language : en
Publisher: World Scientific
Release Date : 2008
Recent Advances In Nonlinear Analysis written by Michel Chipot and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume considers the most recent advances in various topics in partial differential equations. Many important issues such as evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles make this book both a source of inspiration and reference for future research.