| Description |
1 online resource (xii, 235 pages) |
| Series |
London Mathematical Society lecture note series ; 278 |
|
London Mathematical Society lecture note series ; 278.
|
| Contents |
Ch. 1. Preliminary Concepts -- 1.1. Elements of stability theory -- 1.2. Inequalities. Elliptic operators -- 1.3. Sectorial operators -- Ch. 2. The abstract Cauchy problem -- 2.1. Evolutionary equation with sectorial operator -- 2.2. Variation of constants formula -- 2.3. Local X[superscript [alpha]] solutions -- Ch. 3. Semigroups of global solutions -- 3.1. Generation of nonlinear semigroups -- 3.2. Smoothing properties of the semigroup -- 3.3. Compactness results -- Ch. 4. Construction of the global attractor -- 4.1. Dissipativeness of {T(t)} -- 4.2. Existence of a global attractor -- abstract setting -- 4.3. Global solvability and attractors in X[superscript [alpha]] scales -- Ch. 5. Application of abstract results to parabolic equations -- 5.1. Formulation of the problem -- 5.2. Global solutions via partial information -- 5.3. Existence of a global attractor -- Ch. 6. Examples of global attractors in parabolic problems -- 6.1. Introductory example -- 6.2. Single second order dissipative equation -- 6.3. The method of invariant regions -- 6.4. The Cahn-Hilliard pattern formation model -- 6.5. Burgers equation -- 6.6. Navier-Stokes equations in low dimension (n [less than or equal to] 2) -- 6.7. Cauchy problems in the half-space R[superscript +] x R[superscript n] -- Ch. 7. Backward uniqueness and regularity of solutions -- 7.1. Invertible processes -- 7.2. X[superscript s+[alpha]] solutions; s [greater than or equal to] 0, [alpha][Epsilon](0,1) -- Ch. 8. Extensions -- 8.1. Non-Lipschitz nonlinearities -- 8.2. Application of the principle of linearized stability -- 8.3. The n-dimensional Navier-Stokes system -- 8.4. Parabolic problems in Holder spaces -- 8.5. Dissipativeness in Holder spaces -- 8.6. Equations with monotone operators -- Ch. 9. Appendix -- 9.1. Notation, definitions and conventions -- 9.2. Abstract version of the maximum principle -- 9.3. L[superscript [infinity]]([Omega]) estimate for second order problems -- 9.4. Comparison of X[superscript [alpha]] solution with other types of solutions -- 9.5. Final remarks |
| Summary |
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations |
| Bibliography |
Includes bibliographical references (pages 225-233) and index |
| Notes |
Print version record |
| Subject |
Attractors (Mathematics)
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Differential equations, Parabolic.
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MATHEMATICS -- Topology.
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Attractors (Mathematics)
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Differential equations, Parabolic
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Parabolische differentiaalvergelijkingen.
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Dynamische systemen.
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Attracteurs (Mathématiques)
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Equations différentielles paraboliques.
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| Form |
Electronic book
|
| Author |
Dlotko, Tomasz
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London Mathematical Society.
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| ISBN |
9781107363120 |
|
1107363128 |
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9780511526404 |
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0511526407 |
|
9781107368033 |
|
1107368030 |
|
