UID:
edocfu_9959240277802883
Format:
1 online resource (xxv, 483 pages) :
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digital, PDF file(s).
ISBN:
1-139-88165-5
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1-107-10236-7
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1-107-08755-4
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1-107-09983-8
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1-107-09378-3
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1-139-08696-0
Series Statement:
Encyclopedia of mathematics and its applications. Section, Analysis ;
Content:
This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.
Note:
Imprint and ISBN from label on t.p. verso. Imprint on t.p.: Reading Mass. : Addison-Wesley, Advanced Book Program, 1984.
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Publication taken over by Cambridge University Press in 1984.
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"Some references to the literature on (u)=u[subscript xx]-u[subscript t]": p. 357-477.
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Includes index.
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Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Editor's Statement; Foreword; Preface; Chapter 0 Preliminaries; 0.0. SOME INEQUALITIES; 0.1. SEQUENCES AND SERIES OF CONTINUOUS FUNCTIONS, THE ASCOLI-ARZELA THEOREM, AND THE WEIERSTRASS APPROXIMATION THEOREM; 0.2. THE LEBESGUE DOMINATED-CONVERGENCE THEOREM, LEIBNIZ'S RULE, AND FUBINI'S THEOREM; 0.3. COMPLEX ANALYSIS; NOTES; REFERENCES; Chapter 1 Introduction; 1.1. DERIVATION OF THE HEAT EQUATION; 1.2. EQUATIONS REDUCIBLE TO THE HEAT EQUATION; 1.3. ELEMENTARY SOLUTIONS; 1.4. METHODS OF GENERATING SOLUTIONS FROM SOLUTIONS
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1.5. BASIC DEFINITIONS1.6. THE WEAK MAXIMUM PRINCIPLE AND SOME APPLICATIONS; EXERCISES; NOTES; REFERENCES; Chapter 2 The Cauchy Problem; 2.1. INTRODUCTION; 2.2. THE HOLMGREN FUNCTION CLASSES; 2.3. AN EXISTENCE THEOREM; 2.4. AN EXAMPLE; 2.5. CONTINUOUS DEPENDENCE UPON THE DATA; 2.6. VARIABLE DATA-BEARING CURVES: EXISTENCE: AN EXERCISE; NOTES; REFERENCES; Chapter 3 The Initial-Value Problem; 3.1. INTRODUCTION; 3.2. THE FUNDAMENTAL SOLUTION K(x, t); 3.3. CONVERGENCE OF THE CONVOLUTION u(x,t)=Jœ~œk(x-ξ,T)f(ξ)dξ; 3.4. LIMt!ou(x, t); 3.5. AN EXISTENCE THEOREM; 3.6. UNIQUENESS; 3.7. NONUNIQUENESS
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EXERCISESChapter 4 The Initial-Boundary-Value Problem for the Quarter Plane with Temperature-Boundary Specification; 4.1. INTRODUCTION; 4.2. PROPERTIES OF THE CONVOLUTION w(x, t) = - 2j~( jk/ jx)(x, t - 't)g( 't) d't; 4.3. AN EXISTENCE THEOREM; 4.4. UNIQUENESS AND NONUNIQUENESS; EXERCISES; Chapter 5 The Initial-Boundary-Value Problem for the Quarter Plane with Heat-Flux-Boundary Specification; 5.1. EXISTENCE; 5.2. UNIQUENESS; 5.3. NONUNIQUENESS; EXERCISES
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Chapter 6 The Initial-Boundary-Value Problem for the Semi-Infinite Strip with Temperature-Boundary Specification and Heat-Flux-Boundary Specification6.1. INTRODUCTION; 6.2. SOMEPROPERTIES OF o(x,t)=Σœ~ __ ook(x+2m,t); 6.3. AN EXISTENCE AND UNIQUENESS THEOREM; 6.4. SPECIFICATION OF HEAT FLUX ON THE BOUNDARY; 6.5. REDUCTION TO A SYSTEM OF INTEGRAL EQUATIONS; NOTES ON ChapterS 3-6; REFERENCESFOR ChapterS 3-6; Chapter 7 The Reduction of Some Initial-Boundary-Value Problems for the Semi-Infinite Strip, to Integral Equations: Some Exercises; 7.1. THE BOUNDARY CONDITION u(0, t) WITH ux(1, t)
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7.2. THE BOUNDARY CONDITION ux〈o, t)+ a(t)u(o, t) with u(l, t)7.3. THE BOUNDARY CONDITION ux(o, t) = f(t, u(o, t» with ux (l, t); 7.4. THE BOUNDARY CONDITION ur(o, t)+ a(t)ux(o, t) + fi(t)u(o, t) with u(l, t); 7.5. THE BOUNDARY CONDITION jo(t)u(x, t) dx with u(l, t); NOTES; REFERENCES; Chapter 8 Integral Equations; 8.1. VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND AND THE ABEL INTEGRAL EQUATION; 8.2. VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND; 8.3. CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF INTEGRAL EQUATIONS UPON THE DATA; 8.4. A PRIORI BOUNDS ON SOLUTIONS OF INTEGRAL EQUATIONS
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EXERCISES
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English
Additional Edition:
ISBN 0-521-08944-1
Additional Edition:
ISBN 0-521-30243-9
Language:
English
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