Nonlinear Evolution Equations - Global Behavior of Solutions
Author: Alain Haraux
Publisher: Springer
Published: 2006-11-15
Total Pages: 324
ISBN-13: 3540385347
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Author: Alain Haraux
Publisher: Springer
Published: 2006-11-15
Total Pages: 324
ISBN-13: 3540385347
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 2012
Total Pages: 216
ISBN-13: 9781536117165
DOWNLOAD EBOOKAuthor: Songmu Zheng
Publisher: CRC Press
Published: 2004-07-08
Total Pages: 304
ISBN-13: 0203492226
DOWNLOAD EBOOKNonlinear 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: Gaston M. N'Guérékata
Publisher:
Published: 2012
Total Pages: 0
ISBN-13: 9781616684259
DOWNLOAD EBOOKThis 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: Baoxiang Wang
Publisher: World Scientific
Published: 2011-08-10
Total Pages: 298
ISBN-13: 9814458392
DOWNLOAD EBOOKThis 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: Peter J. Olver
Publisher: Springer Science & Business Media
Published: 2013-11-08
Total Pages: 636
ISBN-13: 3319020994
DOWNLOAD EBOOKThis 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: Kazufumi Ito
Publisher: World Scientific
Published: 2002
Total Pages: 524
ISBN-13: 9789812380265
DOWNLOAD EBOOKAnnotation 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: Behzad Djafari Rouhani
Publisher: CRC Press
Published: 2019-05-20
Total Pages: 450
ISBN-13: 148222819X
DOWNLOAD EBOOKThis book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors.
Author: Sandra Carillo
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 247
ISBN-13: 3642840396
DOWNLOAD EBOOKNonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.
Author: Nina B. Maslova
Publisher: World Scientific
Published: 1993
Total Pages: 210
ISBN-13: 9789810211622
DOWNLOAD EBOOKThe 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.