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Nonlinear hyperbolic partial differential equations

Author： Yuzhu Wang, Fagui Liu
Impression：1-2
ISBN：9787302453765
Subject：Basic Sciences
Publication Date：2016.12.01
Page Count：216

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This book is concerned mainly with the initial value problem for nonlinear hyperbolic partial differential equations. Some basic methods and techniques of studying hyperbolic equations are presented. In the book, global existence , singularities , blow up and life span of classical solutions to hyperbolic equations are discussed. Some related problems for hyperbolic geometric flow on Riemann surfaces are studied. The book can be used for students and postgraduates majoring in mathematics, teachers，scientists and engineers.

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Preface ...................................................................................................I _x000D_ Chapter 1 Introduction..................................................................... 1 _x000D_ 1.1 Intention and Signi.cances ....................................................... 1 _x000D_ 1.2 Basic Concepts ........................................................................ 7 _x000D_ 1.3 Some Examples.......................................................................14 _x000D_ 1.4 Preliminaries ..........................................................................18 _x000D_ Chapter 2 Cauchy Problem for Nonlinear Hyperbolic Systems in Diagonal Form ...........................................................25 _x000D_ 2.1 The Single Nonlinear Hyperbolic Equation ...............................25 _x000D_ 2.2 The Classical Solutions to Single Nonlinear Hyperbolic Equation ................................................................................32 _x000D_ 2.3 Nonlinear Hyperbolic Equations in Diagonal Form....................40 _x000D_ Chapter 3 Singularities Caused by the Eigenvectors ....................50 _x000D_ 3.1 Introduction ...........................................................................50 _x000D_ 3.2 Completely Reducible Systems.................................................55 _x000D_ 3.3 2-Step Completely Reducible Systems ......................................59 _x000D_ 3.4 m(m> 2)-Step Completely Reducible Systems with Constant Eigenvalues ..............................................................67 _x000D_ 3.5 Non-completely Reducible Systems ..........................................74 _x000D_ 3.6 Examples ...............................................................................76 _x000D_ Chapter 4 Hyperbolic Geometric Flow on Riemannian Surfaces...........................................................................85 _x000D_ 4.1 Introduction ...........................................................................85 _x000D_ 4.2 Cauchy Problem for Hyperbolic Geometric Flow.......................87 _x000D_ 4.3 Mixed Initial Boundary Value Problem for Hyperbolic Geometric Flow ......................................................................99 _x000D_ 4.4 Dissipative Hyperbolic Geometric Flow .................................. 107 _x000D_ 4.5 Explicit Solutions..................................................................119 _x000D_ 4.6 Radial Solutions to Hyperbolic Geometric Flow ...................... 124 _x000D_ Chapter 5 Life-Span of Classical Solutions to Hyperbolic Geometric Flow in Two Space Variables with Slow Decay Initial Data .............................................. 127 _x000D_ 5.1 Intention and Signi.cances .................................................... 127 _x000D_ 5.2 Some Useful Lemmas ............................................................ 130 _x000D_ 5.3 Lower Bound of Life-Span ..................................................... 143 _x000D_ Chapter 6 Nonlinear Hyperbolic Systems with Relaxation ...... 153 _x000D_ 6.1 Introduction ......................................................................... 153 _x000D_ 6.2 Global Classical Solutions...................................................... 155 _x000D_ 6.3 Applications .........................................................................162 _x000D_ 6.4 Convergence of Approximate Solutions...................................165 _x000D_ Chapter 7 Applications.................................................................. 175 _x000D_ 7.1 One Dimensional Hydromagnetic Dynamics............................175 _x000D_ 7.2 Fluid Flow on a Pipe ............................................................ 187 _x000D_ 7.3 Heat Conduction with Finite of Propagation .......................... 189 _x000D_ 7.4 A Nonlinear Systems in Viscoelasticity...................................191 _x000D_ Bibliography ...................................................................................... 202 _x000D_ Index .................................................................................................. 209 _x000D_ _x000D_ _x000D_ _x000D_ _x000D_