Approximation of nonlinear evolution systems
Approximation of nonlinear evolution systems
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
New York
Academic Press
1983, 1983
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| Series: | Mathematics in science and engineering
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- 3.0 Introduction3.1 General Operator Results in Banach Spaces and Ordered Spaces; 3.2 Applications and Examples; 3.3 Semidiscretizations Defined by Quadrature; 3.4 Bibliographical Remarks; References; Chapter 4. Numerical Optimality and the Approximate Solution of Degenerate Parabolic Equations; 4.0 Introduction; 4.1 Representations of Sobolev-Type and Upper-Bound Estimates; 4.2 Lower-Bound Estimates and N-Widths; 4.3 Convergence Rates for the Continuous Galerkin Method; 4.4 Convergence Rates for Semidiscrete Approximations; 4.5 Bibliographical Remarks; References
- Includes bibliographical references and index
- Chapter 5. Existence Analysis via the Stability of Consistent Semidiscrete Approximations5.0 Introduction; 5.1 Stability in Sobolev Norms for Semidiscretizations of Degenerate Parabolic Equations; 5.2 Existence of Weak Solutions for the Stefan Problem and the Porous-Medium Equation and Approximation Results; 5.3 Existence for Reaction-Diffusion Systems; 5.4 Existence for the Generalized Form of the Navier-Stokes Equations for Incompressible Fluids; 5.5 Bibliographical Remarks; References; PART II: LOGCAL SMOOTH SOLUTIONS; Chapter 6. Linear Evolution Operators; 6.0 Introduction
- 1.6 Bibliographical RemarksReferences; Chapter 2. Convergent Regularizations and Pointwise Stability of Implicit Schemes; 2.0 Introduction; 2.1 Regularization in the Stefan Problem; 2.2 Semidiscrete Regularization and Maximum Principles in the Stefan Problem; 2.3 Regularization in the Porous-Medium Equation; 2.4 Nonnegative Semidiscrete Solutions of Porous-Medium Equation and Maximum Principles; 2.5 Invariant Rectangles and Maximum Principles for Reaction-Diffusion Systems in Semidiscrete Form; 2.6 Bibliographical Remarks; References; Chapter 3. Nonlinear Elliptic Equations and Inequalities
- 6.1 Semigroup Preliminaries6.2 The Linear Evolution Equation and Evolution Operators; 6.3 Peturbations of Generators and Regularity of Evolution Operators; 6.4 The Inhomogeneous Problem and an Application to Linear Symmetric Hyperbolic Systems; 6.5 Bibliographical Remarks; References; Chapter 7. Quasi-linear Equations of Evolution; 7.0 Introduction; 7.1 Perturbation of the Linear Problem and Nonlinear Preliminaries; 7.2 The Quasi-linear Cauchy Problem in Banach Space; 7.3 Quasi-linear Second-Order Hyperbolic Systems; 7.4 The Vacuum Field Equations of General Relativity
- Front Cover; Approximation of Nonlinear Evolution Systems; Copyright Page; Contents; Preface; Acknowledgments; List of Symbols and Definitions; Introduction; PART I: GLOBAL WEAK SOLUTIONS; Chapter 1. Problem Formulations and Uniqueness for Dissipative Parabolic Models; 1.0 Introduction; 1.1 Heat Conduction with Change of Phase: Stefan Problems; 1.2 Unsaturated Fluid Infiltration in Porous Media; 1.3 Reaction-Diffusion Systems; 1.4 Incompressible, Viscous Fluid Dynamics at Constant Temperature: Navier-Stokes Equations and Generalizations; 1.5 Uniqueness of Solutions