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Linear And Quasi Linear Equations Of Parabolic Type
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Book Synopsis Linear and Quasi-linear Equations of Parabolic Type by : Olʹga A. Ladyženskaja
Download or read book Linear and Quasi-linear Equations of Parabolic Type written by Olʹga A. Ladyženskaja and published by American Mathematical Soc.. This book was released on 1988 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Book Synopsis Linear and Quasilinear Parabolic Problems by : Herbert Amann
Download or read book Linear and Quasilinear Parabolic Problems written by Herbert Amann and published by Birkhäuser. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear and quasi-linear equations of parabolic type by : Olga Aleksandrovna Ladyzenskaja
Download or read book Linear and quasi-linear equations of parabolic type written by Olga Aleksandrovna Ladyzenskaja and published by . This book was released on 1988 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Fuensanta Andreu-Vaillo Publisher :Springer Science & Business Media ISBN 13 :9783764366193 Total Pages :368 pages Book Rating :4.3/5 (661 download)
Book Synopsis Parabolic Quasilinear Equations Minimizing Linear Growth Functionals by : Fuensanta Andreu-Vaillo
Download or read book Parabolic Quasilinear Equations Minimizing Linear Growth Functionals written by Fuensanta Andreu-Vaillo and published by Springer Science & Business Media. This book was released on 2004-01-26 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Linear and Quasi-linear Evolution Equations in Hilbert Spaces by : Pascal Cherrier
Download or read book Linear and Quasi-linear Evolution Equations in Hilbert Spaces written by Pascal Cherrier and published by American Mathematical Soc.. This book was released on 2012-07-18 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers evolution equations of hyperbolic and parabolic type. These equations are studied from a common point of view, using elementary methods, such as that of energy estimates, which prove to be quite versatile. The authors emphasize the Cauchy problem and present a unified theory for the treatment of these equations. In particular, they provide local and global existence results, as well as strong well-posedness and asymptotic behavior results for the Cauchy problem for quasi-linear equations. Solutions of linear equations are constructed explicitly, using the Galerkin method; the linear theory is then applied to quasi-linear equations, by means of a linearization and fixed-point technique. The authors also compare hyperbolic and parabolic problems, both in terms of singular perturbations, on compact time intervals, and asymptotically, in terms of the diffusion phenomenon, with new results on decay estimates for strong solutions of homogeneous quasi-linear equations of each type. This textbook presents a valuable introduction to topics in the theory of evolution equations, suitable for advanced graduate students. The exposition is largely self-contained. The initial chapter reviews the essential material from functional analysis. New ideas are introduced along with their context. Proofs are detailed and carefully presented. The book concludes with a chapter on applications of the theory to Maxwell's equations and von Karman's equations.
Book Synopsis Second Order Equations of Elliptic and Parabolic Type by : E. M. Landis
Download or read book Second Order Equations of Elliptic and Parabolic Type written by E. M. Landis and published by American Mathematical Soc.. This book was released on 1997-12-02 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.
Book Synopsis Nonlinear Parabolic and Elliptic Equations by : C.V. Pao
Download or read book Nonlinear Parabolic and Elliptic Equations written by C.V. Pao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Author :Emmanuele DiBenedetto Publisher :Springer Science & Business Media ISBN 13 :1461208955 Total Pages :402 pages Book Rating :4.4/5 (612 download)
Book Synopsis Degenerate Parabolic Equations by : Emmanuele DiBenedetto
Download or read book Degenerate Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolved 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.
Book Synopsis Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order by : A. V. Ivanov
Download or read book Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order written by A. V. Ivanov and published by American Mathematical Soc.. This book was released on 1984 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear and Quasilinear Parabolic Problems by : Herbert Amann
Download or read book Linear and Quasilinear Parabolic Problems written by Herbert Amann and published by Springer Science & Business Media. This book was released on 1995-03-27 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.
Book Synopsis Elliptic and Parabolic Equations with Discontinuous Coefficients by : Antonino Maugeri
Download or read book Elliptic and Parabolic Equations with Discontinuous Coefficients written by Antonino Maugeri and published by Wiley-VCH. This book was released on 2000-12-13 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parabolic Quasilinear Equations Minimizing Linear Growth Functionals by : Fuensanta Andreu-Vaillo
Download or read book Parabolic Quasilinear Equations Minimizing Linear Growth Functionals written by Fuensanta Andreu-Vaillo and published by Birkhäuser. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type by : Samuil D. Eidelman
Download or read book Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type written by Samuil D. Eidelman and published by Birkhäuser. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations. It will appeal to mathematicians interested in new classes of partial differential equations, and physicists specializing in diffusion processes.
Book Synopsis Second Order Parabolic Differential Equations by : Gary M. Lieberman
Download or read book Second Order Parabolic Differential Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 1996 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Book Synopsis Linear and Quasilinear Elliptic Equations by : Ladyzhenskaya
Download or read book Linear and Quasilinear Elliptic Equations written by Ladyzhenskaya and published by Academic Press. This book was released on 1968 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear and Quasilinear Elliptic Equations
Book Synopsis Recent Advances in Nonlinear Analysis by : Michel Chipot
Download or read book Recent Advances in Nonlinear Analysis written by Michel Chipot and published by World Scientific. This book was released on 2008 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Partial Differential Equations by : Marcelo Epstein
Download or read book Partial Differential Equations written by Marcelo Epstein and published by Springer. This book was released on 2017-04-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.
