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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Linear and Nonlinear Evolution Equations
Nonlinear Evolution Equations
Author: Songmu Zheng
Publisher: CRC Press
Published: 2004-07-08
Total Pages: 304
ISBN-13: 0203492226
DOWNLOAD EBOOK →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
Linear and Nonlinear Evolution Equations
Author: Gaston M. N'Guérékata
Publisher:
Published: 2012
Total Pages: 0
ISBN-13: 9781616684259
DOWNLOAD EBOOK →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.
Harmonic Analysis Method For Nonlinear Evolution Equations, I
Author: Baoxiang Wang
Publisher: World Scientific
Published: 2011-08-10
Total Pages: 298
ISBN-13: 9814458392
DOWNLOAD EBOOK →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.
Introduction to Partial Differential Equations
Author: Peter J. Olver
Publisher: Springer Science & Business Media
Published: 2013-11-08
Total Pages: 636
ISBN-13: 3319020994
DOWNLOAD EBOOK →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.
Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces
Author: Behzad Djafari Rouhani
Publisher: CRC Press
Published: 2019-05-20
Total Pages: 450
ISBN-13: 148222819X
DOWNLOAD EBOOK →This 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.
Nonlinear Evolution Equations and Dynamical Systems
Author: Sandra Carillo
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 247
ISBN-13: 3642840396
DOWNLOAD EBOOK →Nonlinear 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.
Lectures on Nonlinear Evolution Equations
Author: Reinhard Racke
Publisher: Birkhäuser
Published: 2015-08-31
Total Pages: 315
ISBN-13: 3319218735
DOWNLOAD EBOOK →This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.
Nonlinear Evolution Equations and Related Topics
Author: Wolfgang Arendt
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 803
ISBN-13: 3034879245
DOWNLOAD EBOOK →Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
