UID:
almahu_9947367625402882
Format:
1 online resource (609 p.)
ISBN:
1-281-79576-3
,
9786611795764
,
0-08-093197-9
Series Statement:
Handbook of Differential Equations: Evolutionary Equations
Content:
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Note:
Description based upon print version of record.
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Front cover; Handbook of Differential Equations: Evolutionary Equations; Copyright page; Preface; List of Contributors; Contents; Contents of Volume I; Contents of Volume II; Contents of Volume III; Chapter 1. Incompressible Euler Equations: The Blow-up Problem and Related Results; 1. Introduction; 2. Local well-posedness and blow-up criteria; 3. Blow-up scenarios; 4. Model problems; 5. Dichotomy: singularity or global regular dynamics?; 6. Spectral dynamics approach; 7. Conservation laws for singular solutions; References; Chapter 2. Mathematical Methods in the Theory of Viscous Fluids
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1. Balance laws2. Formulation of basic physical principles; 3. Constitutive theory; 4. A priori estimates; 5. Weak sequential stability; 6. Long-time behavior; 7. Singular limits; References; Chapter 3. Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains; 1. Introduction; 2. The global attractor; 3. Exponential attractors; 4. Nonautonomous systems; 5. Dissipative PDEs in unbounded domains; 6. Ill-posed dissipative systems and trajectory attractors; References; Chapter 4. The Cahn-Hilliard Equation; 1. Introduction
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2. Backwards diffusion and regularization3. The Cahn-Hilliard equation and phase separation; 4. Two prototype formulations; 5. Existence, uniqueness, and regularity; 6. Linear stability and spinodal decomposition; 7. Comparison with experiment; 8. Long time behavior and limiting motions; 9. Upper bounds for coarsening; Acknowledgements; References; Chapter 5. Mathematical Analysis of Viscoelastic Fluids; 1. The equations describing viscoelastic flows; 2. Existence results for initial value problems; 3. Development of singularities; 4. Steady flows; 5. Instabilities and change of type
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6. Controllability of viscoelastic flows7. Concluding remarks; References; Chapter 6. Application of Monotone Type Operators to Parabolic and Functional Parabolic PDE's; 1. Introduction; 2. Abstract Cauchy problem for first order evolution equations; 3. Second order and higher order nonlinear parabolic differential equations; 4. Parabolic functional differential equations containing functional dependence in lower order terms; 5. Parabolic equations containing functional dependence in the main part; 6. Parabolic functional differential equations in (0,); 7. Further applications; References
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Chapter 7. Recent Results on Hydrodynamic Limits1. Introduction; 2. Fluid equations, relative entropy, and dissipative solutions; 3. Kinetic equations; 4. Hydrodynamic limits; 5. Conclusion and open problems; Acknowledgements; References; Chapter 8. Introduction to Stefan-Type Problems; 0. Introduction; 1. The Stefan model; 2. More general models of phase transitions; 3. Analysis of the weak formulation of the Stefan model; 4. Phase relaxation with nonlinear heat diffusion; 5. Convexity and other analytical tools; Acknowledgments; 6. Bibliography; References; Chapter 9. The KdV Equation
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1. Historical background
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English
Additional Edition:
ISBN 0-444-53034-7
Language:
English
