Nonlinear Evolution Equations - Global Behavior of Solutions PDF Download

Author: Alain Haraux
Publisher: Springer
ISBN: 3540385347
Category : Mathematics
Languages : en
Pages : 324

View

Book Description

Author: Gaston M. N'Guérékata
Publisher:
ISBN: 9781616684259
Category : Evolution equations
Languages : en
Pages : 0

View

Book Description
This book presents and discusses current research in the study of linear and non-linear evolution equations. Topics discussed include semi-linear abstract differential equations; singular solutions of a semi-linear elliptic equation on non-smooth domains; non-linear parabolic systems with non-linear boundaries; the decay of solutions of a non-linear BBM-Burgers System and critical curves for a degenerate parabolic system with non-linear boundary conditions.

Author: Kazufumi Ito
Publisher: World Scientific
ISBN: 9789812380265
Category : Science
Languages : en
Pages : 524

View

Book Description
Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR

Author: Peter J. Olver
Publisher: Springer Science & Business Media
ISBN: 3319020994
Category : Mathematics
Languages : en
Pages : 636

View

Book Description
This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

Author: Baoxiang Wang
Publisher: World Scientific
ISBN: 9814458392
Category : Mathematics
Languages : en
Pages : 298

View

Book Description
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

Author: Alexander L. Sakhnovich
Publisher: Walter de Gruyter
ISBN: 3110258617
Category : Mathematics
Languages : en
Pages : 356

View

Book Description
This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

Author: Songmu Zheng
Publisher: CRC Press
ISBN: 0203492226
Category : Mathematics
Languages : en
Pages : 303

View

Book Description
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator

Author: Nina B. Maslova
Publisher: World Scientific
ISBN: 9789810211622
Category : Mathematics
Languages : en
Pages : 210

View

Book Description
The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.

Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 0521387302
Category : Mathematics
Languages : en
Pages : 532

View

Book Description
This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Author: Robert M. Miura
Publisher: Springer
ISBN: 3540382208
Category : Mathematics
Languages : en
Pages : 302

View

Book Description
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974