UID:
almahu_9949697977902882
Format:
1 online resource (231 p.)
ISBN:
1-282-28915-2
,
9786612289156
,
0-08-095594-0
Series Statement:
Mathematics in science and engineering ; v. 85
Content:
Differential equations in abstract spaces
Note:
Description based upon print version of record.
,
Front Cover; Differential Equations in Abstract Spaces; Copyright Page; Contents; Preface; Acknowledgments; Chapter 1. The Calculus of Abstract Functions; 1.0 Introduction; 1.1 Abstract Functions; 1.2 The Mean Value Theorem; 1.3 The Riemann Integral Abstract Functions; 1.4 Abstract Lebesgue Integrals; 1.5 The Abstract Stieltjes Integral; 1.6 Gateaux and Fréchet Differentials; 1.7 Notes; Chapter 2. Semigroups of Operators; 2.0 Introduction; 2.1 Strongly Continuous Semigroups of Operators; 2.2 The Infinitesimal Generator; 2.3 The Hille-Yosida-Phillips Theorem
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2.4 Linear Autonomous Funtional Differential Equations2.5 Analytic Semigroups; 2.6 Notes; Chapter 3. Linear Evolution Equations of the Parabolic Type: Sobolevski-Tanabe Theory; 3.0 Introduction; 3.1 Definitions and Hypotheses; 3.2 Statements of the Main Theorems and Some Heuristic Arguments; 3.3 Properties of the Semigroup {exo[-tA(t)]}; 3.4 Existence of a Fundamental Solution; 3.5 Uniqueness of the Fundamental Solution; 3.6 Solution of the Abstract Cauchy Problem; 3.7 Differentiability of Solutions; 3.8 Asymptotic Behavior; 3.9 Notes; Chapter 4. Evolution Inequalities; 4.0 Introduction
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4.1 Lower Bounds, Uniqueness, and Convexity (Special Results)4.2 Lower Bounds, Uniqueness, and Convexity (General Results); 4.3 Approximate Solutions, Bounds, and Uniqueness; 4.4 Application to Parabolic Equations; 4.5 Notes; Chapter 5. Nonlinear Differential Equations; 5.0 Introduction; 5.1 Counterexamples; 5.2 Existence and Uniqueness; 5.3 Nonlinear Variation of Constants Formula; 5.4 Stability and Asymptotic Behavior; 5.5 Chaplygin's Method; 5.6 Global Existence and Asymptotic Equilibrium; 5.7 Lyapunov Functions and Stability Criteria; 5.8 Notes; Chapter 6. Special Topics; 6.0 Introduction
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6.1 Nonlinear Semigroups and Differential Equations6.2 Functional Differential Equations in Banach Spaces; 6.3 Second-Order Evolution Equations; 6.4 Notes; Appendixes; Bibliography; Index
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English
Additional Edition:
ISBN 0-12-432650-1
Language:
English
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