Strong Maximum Principle for a Quasi-linear Equation with Applications
| Author | : Seppo Granlund |
| Publisher | : |
| Total Pages | : 468 |
| Release | : 1978 |
| Genre | : Differential equations, Elliptic |
| ISBN | : |
Strong Maximum Principle For A Quasi Linear Equation With Applications
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Proceedings of the Conference on Differential & Difference Equations and Applications
| Author | : Ravi P. Agarwal |
| Publisher | : Hindawi Publishing Corporation |
| Total Pages | : 1266 |
| Release | : 2006 |
| Genre | : Difference equations |
| ISBN | : 9789775945389 |
Handbook of Differential Equations: Stationary Partial Differential Equations
| Author | : Michel Chipot |
| Publisher | : Elsevier |
| Total Pages | : 627 |
| Release | : 2007-05-03 |
| Genre | : Mathematics |
| ISBN | : 0080521835 |
A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.- written by well-known experts in the field- self contained volume in series covering one of the most rapid developing topics in mathematics
Blow-Up in Quasilinear Parabolic Equations
| Author | : A. A. Samarskii |
| Publisher | : Walter de Gruyter |
| Total Pages | : 561 |
| Release | : 2011-06-24 |
| Genre | : Mathematics |
| ISBN | : 3110889862 |
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Linear and Quasilinear Parabolic Problems
| 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.
The Ricci Flow: Techniques and Applications
| Author | : Bennett Chow |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 542 |
| Release | : 2010-04-21 |
| Genre | : Mathematics |
| ISBN | : 0821846612 |
The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.
The Einstein Equations and the Large Scale Behavior of Gravitational Fields
| Author | : Piotr T. Chrusciel |
| Publisher | : Birkhäuser |
| Total Pages | : 487 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034879539 |
The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
Variational, Topological, and Partial Order Methods with Their Applications
| Author | : Zhitao Zhang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2012-09-18 |
| Genre | : Mathematics |
| ISBN | : 3642307086 |
Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
The Conformal Structure of Space-Times
| Author | : Jörg Frauendiener |
| Publisher | : Springer |
| Total Pages | : 382 |
| Release | : 2008-01-11 |
| Genre | : Science |
| ISBN | : 3540458182 |
Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.
A Course on Partial Differential Equations
| Author | : Walter Craig |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 217 |
| Release | : 2018-12-12 |
| Genre | : Mathematics |
| ISBN | : 1470442922 |
Does entropy really increase no matter what we do? Can light pass through a Big Bang? What is certain about the Heisenberg uncertainty principle? Many laws of physics are formulated in terms of differential equations, and the questions above are about the nature of their solutions. This book puts together the three main aspects of the topic of partial differential equations, namely theory, phenomenology, and applications, from a contemporary point of view. In addition to the three principal examples of the wave equation, the heat equation, and Laplace's equation, the book has chapters on dispersion and the Schrödinger equation, nonlinear hyperbolic conservation laws, and shock waves. The book covers material for an introductory course that is aimed at beginning graduate or advanced undergraduate level students. Readers should be conversant with multivariate calculus and linear algebra. They are also expected to have taken an introductory level course in analysis. Each chapter includes a comprehensive set of exercises, and most chapters have additional projects, which are intended to give students opportunities for more in-depth and open-ended study of solutions of partial differential equations and their properties.
