Asymptotics for Dissipative Nonlinear Equations

Asymptotics for Dissipative Nonlinear Equations
Title Asymptotics for Dissipative Nonlinear Equations PDF eBook
Author Nakao Hayashi
Publisher Springer Science & Business Media
Pages 570
Release 2006-04-21
Genre Mathematics
ISBN 3540320598

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Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

Asymptotics for Dissipative Nonlinear Equations

Asymptotics for Dissipative Nonlinear Equations
Title Asymptotics for Dissipative Nonlinear Equations PDF eBook
Author
Publisher
Pages 557
Release 2006
Genre Equations
ISBN

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Asymptotic Behavior of Dissipative Systems

Asymptotic Behavior of Dissipative Systems
Title Asymptotic Behavior of Dissipative Systems PDF eBook
Author Jack K. Hale
Publisher American Mathematical Soc.
Pages 210
Release 2010-01-04
Genre Mathematics
ISBN 0821849344

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This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.

Mathematical Results in Quantum Mechanics

Mathematical Results in Quantum Mechanics
Title Mathematical Results in Quantum Mechanics PDF eBook
Author Pavel Exner
Publisher American Mathematical Soc.
Pages 362
Release 2002
Genre Mathematics
ISBN 0821829009

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This work contains contributions presented at the conference, QMath-8: Mathematical Results in Quantum Mechanics'', held at Universidad Nacional Autonoma de Mexico in December 2001. The articles cover a wide range of mathematical problems and focus on various aspects of quantum mechanics, quantum field theory and nuclear physics. Topics vary from spectral properties of the Schrodinger equation of various quantum systems to the analysis of quantum computation algorithms. The book should be suitable for graduate students and research mathematicians interested in the mathematical aspects of quantum mechanics.

Selected Papers on Analysis and Differential Equations

Selected Papers on Analysis and Differential Equations
Title Selected Papers on Analysis and Differential Equations PDF eBook
Author 野水克己
Publisher American Mathematical Soc.
Pages 152
Release 2003
Genre Differential equations, Partial
ISBN 9780821835081

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This volume contains translations of papers that originally appeared in the Japanese journal, Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including nonlinear partial differential equations, $C*$-algebras, and Schrodinger operators. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.

Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations

Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
Title Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations PDF eBook
Author Valery V. Kozlov
Publisher Springer Science & Business Media
Pages 278
Release 2013-01-13
Genre Mathematics
ISBN 3642338178

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The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.

Analytic Inequalities and Their Applications in PDEs

Analytic Inequalities and Their Applications in PDEs
Title Analytic Inequalities and Their Applications in PDEs PDF eBook
Author Yuming Qin
Publisher Birkhäuser
Pages 570
Release 2017-02-13
Genre Mathematics
ISBN 3319008315

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This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.