Vanishing viscosity method : solutions to nonlinear systems
Viscosity solutions e-böcker
Walter de Gruyter GmbH
2017
EISBN 9783110492576
1 Sobolev Space and Preliminaries ; 1.1 Basic Notation and Function Spaces ; 1.1.1 Basic Notation ; 1.1.2 Function Spaces ; 1.1.3 Some Basic Inequalities ; 1.2 Weak Derivatives and Its Properties, Wm p (K) and Hj, p(K) Spaces.
1.3 Sobolev Embedding Theorem and Interpolation Formula 1.4 Compactness Theory ; 1.5 Fixed Point Principle ; 2 The Vanishing Viscosity Method of Some Nonlinear Evolution System ; 2.1 Periodic Boundary and Cauchy Problem for High-Order Generalized KdV System in Dimension One.
2.2 Some KdV System with High-Order Derivative Term 2.3 High-Order Multivariable KdV Systems and Hirota Coupled KdV Systems ; 2.4 Initial Boundary Value Problem for Ferrimagnetic Equations.
2.7 Initial Value Problem for the Nonlinear Singular Integral and Differential Equations in Deep Water 2.8 Initial Value Problem for the Nonlinear Schrödinger Equations ; 2.9 Initial Value Problem and Boundary Value Problem for the Nonlinear Schrödinger Equation with Derivative.
"The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science."--Resource home page
1.3 Sobolev Embedding Theorem and Interpolation Formula 1.4 Compactness Theory ; 1.5 Fixed Point Principle ; 2 The Vanishing Viscosity Method of Some Nonlinear Evolution System ; 2.1 Periodic Boundary and Cauchy Problem for High-Order Generalized KdV System in Dimension One.
2.2 Some KdV System with High-Order Derivative Term 2.3 High-Order Multivariable KdV Systems and Hirota Coupled KdV Systems ; 2.4 Initial Boundary Value Problem for Ferrimagnetic Equations.
2.7 Initial Value Problem for the Nonlinear Singular Integral and Differential Equations in Deep Water 2.8 Initial Value Problem for the Nonlinear Schrödinger Equations ; 2.9 Initial Value Problem and Boundary Value Problem for the Nonlinear Schrödinger Equation with Derivative.
"The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science."--Resource home page
