Second Order Linear Differential Equations in Banach Spaces ( Volume 108 )

Publication series ：Volume 108

Author： Fattorini   H. O.  

Publisher： Elsevier Science‎

Publication year： 2011

E-ISBN: 9780080872193

P-ISBN(Paperback): 9780444876980

P-ISBN(Hardback):  9780444876980

Subject： O175.2 Partial Differential Equations

Language： ENG

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Description

Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

Chapter

Front Cover

pp.：  1 – 4

Second Order Linear Differential Equations in Banach Spaces

pp.：  4 – 5

Copyright Page

pp.：  5 – 10

PREFACE

pp.：  6 – 14

Contents

pp.：  10 – 6

LIST OF SYMBOLS

pp.：  14 – 16

CHAPTER I. THE CAUCHY PROBLEM FOR FIRST ORDER EQUATIONS SEMIGROUP THEORY

pp.：  16 – 39

CHAPTER II. THE CAUCHY PROBLEM FOR SECOND ORDER EQUATIONS COSINE FUNCTION THEORY

pp.：  39 – 58

CHAPTER III. REDUCTION OF A SECOND ORDER EQUATION TO A FIRST ORDER SYSTEM. PHASE SPACES

pp.：  58 – 115

CHAPTER IV. APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS

pp.：  115 – 141

CHAPTER V. UNIFORMLY BOUNDED GROUPS AND COSINE FUNCTIONS IN HILBERT SPACE

pp.：  141 – 180

CHAPTER VI. THE PARABOLIC SINGULAR PERTURBATION PROBLEM

pp.：  180 – 253

CHAPTER VII. OTHER SINGULAR PERTURBATION PROBLEMS

pp.：  253 – 285

CHAPTER VIII. THE COMPLETE SECOND ORDER EQUATION

pp.：  285 – 318

BIBLIOGRAPHY

pp.：  318 – 330

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