Linear And Quasi Linear Equations Of Parabolic Type
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| Author | : Olʹga A. Ladyženskaja |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 74 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : 9780821815731 |
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.
| Author | : Herbert Amann |
| Publisher | : Birkhäuser |
| Total Pages | : 366 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034892217 |
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.
| Author | : Olga Aleksandrovna Ladyzenskaja |
| Publisher | : |
| Total Pages | : 648 |
| Release | : 1988 |
| Genre | : |
| ISBN | : |
| Author | : Fuensanta Andreu-Vaillo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 2004-01-26 |
| Genre | : Computers |
| ISBN | : 9783764366193 |
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
| Author | : Olʹga Aleksandrovna Ladyzhenskai︠a︡ |
| Publisher | : |
| Total Pages | : |
| Release | : |
| Genre | : Differential equations |
| ISBN | : |
| Author | : E. M. Landis |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 224 |
| Release | : 1997-12-02 |
| Genre | : Mathematics |
| ISBN | : 9780821897812 |
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.
| Author | : Fuensanta Andreu-Vaillo |
| Publisher | : Birkhäuser |
| Total Pages | : 351 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879288 |
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
| Author | : David Hoff |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2020-11-18 |
| Genre | : Education |
| ISBN | : 1470461617 |
This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
| Author | : Antonino Maugeri |
| Publisher | : Wiley-VCH |
| Total Pages | : 266 |
| Release | : 2000-12-13 |
| Genre | : Mathematics |
| ISBN | : |
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.
| Author | : Herbert Amann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 688 |
| Release | : 1995-03-27 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9783764351144 |
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.
