Global attractors in abstract parabolic problems /:
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Körperschaft: | |
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2000.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
278. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations. |
| Beschreibung: | 1 online resource (xii, 235 pages) |
| Bibliographie: | Includes bibliographical references (pages 225-233) and index. |
| ISBN: | 9781107363120 1107363128 9780511526404 0511526407 9781107368033 1107368030 |
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| 100 | 1 | |a Cholewa, Jan W. | |
| 245 | 1 | 0 | |a Global attractors in abstract parabolic problems / |c Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee. |
| 260 | |a Cambridge, UK ; |a New York : |b Cambridge University Press, |c 2000. | ||
| 300 | |a 1 online resource (xii, 235 pages) | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 278 | |
| 504 | |a Includes bibliographical references (pages 225-233) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations. | ||
| 505 | 0 | |a 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. | |
| 650 | 0 | |a Attractors (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh97005887 | |
| 650 | 0 | |a Differential equations, Parabolic. |0 http://id.loc.gov/authorities/subjects/sh85037909 | |
| 650 | 6 | |a Attracteurs (Mathématiques) | |
| 650 | 6 | |a Équations différentielles paraboliques. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Attractors (Mathematics) |2 fast | |
| 650 | 7 | |a Differential equations, Parabolic |2 fast | |
| 650 | 1 | 7 | |a Parabolische differentiaalvergelijkingen. |2 gtt |
| 650 | 1 | 7 | |a Dynamische systemen. |2 gtt |
| 650 | 7 | |a Attracteurs (Mathématiques) |2 ram | |
| 650 | 7 | |a Equations différentielles paraboliques. |2 ram | |
| 700 | 1 | |a Dlotko, Tomasz. | |
| 710 | 2 | |a London Mathematical Society. |0 http://id.loc.gov/authorities/names/n79118957 | |
| 776 | 0 | 8 | |i Print version: |a Cholewa, Jan W. |t Global attractors in abstract parabolic problems. |d Cambridge, UK ; New York : Cambridge University Press, 2000 |z 0521794242 |w (DLC) 00710511 |w (OCoLC)44014677 |
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| author | Cholewa, Jan W. |
| author2 | Dlotko, Tomasz |
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| author_corporate | London Mathematical Society |
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| 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. |
| ctrlnum | (OCoLC)836869289 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:25:17Z |
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| isbn | 9781107363120 1107363128 9780511526404 0511526407 9781107368033 1107368030 |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Cholewa, Jan W. Global attractors in abstract parabolic problems / Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee. Cambridge, UK ; New York : Cambridge University Press, 2000. 1 online resource (xii, 235 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 278 Includes bibliographical references (pages 225-233) and index. Print version record. This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations. 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. Attractors (Mathematics) http://id.loc.gov/authorities/subjects/sh97005887 Differential equations, Parabolic. http://id.loc.gov/authorities/subjects/sh85037909 Attracteurs (Mathématiques) Équations différentielles paraboliques. MATHEMATICS Topology. bisacsh Attractors (Mathematics) fast Differential equations, Parabolic fast Parabolische differentiaalvergelijkingen. gtt Dynamische systemen. gtt Attracteurs (Mathématiques) ram Equations différentielles paraboliques. ram Dlotko, Tomasz. London Mathematical Society. http://id.loc.gov/authorities/names/n79118957 Print version: Cholewa, Jan W. Global attractors in abstract parabolic problems. Cambridge, UK ; New York : Cambridge University Press, 2000 0521794242 (DLC) 00710511 (OCoLC)44014677 London Mathematical Society lecture note series ; 278. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552516 Volltext |
| spellingShingle | Cholewa, Jan W. Global attractors in abstract parabolic problems / London Mathematical Society lecture note series ; 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. Attractors (Mathematics) http://id.loc.gov/authorities/subjects/sh97005887 Differential equations, Parabolic. http://id.loc.gov/authorities/subjects/sh85037909 Attracteurs (Mathématiques) Équations différentielles paraboliques. MATHEMATICS Topology. bisacsh Attractors (Mathematics) fast Differential equations, Parabolic fast Parabolische differentiaalvergelijkingen. gtt Dynamische systemen. gtt Attracteurs (Mathématiques) ram Equations différentielles paraboliques. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh97005887 http://id.loc.gov/authorities/subjects/sh85037909 |
| title | Global attractors in abstract parabolic problems / |
| title_auth | Global attractors in abstract parabolic problems / |
| title_exact_search | Global attractors in abstract parabolic problems / |
| title_full | Global attractors in abstract parabolic problems / Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee. |
| title_fullStr | Global attractors in abstract parabolic problems / Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee. |
| title_full_unstemmed | Global attractors in abstract parabolic problems / Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee. |
| title_short | Global attractors in abstract parabolic problems / |
| title_sort | global attractors in abstract parabolic problems |
| topic | Attractors (Mathematics) http://id.loc.gov/authorities/subjects/sh97005887 Differential equations, Parabolic. http://id.loc.gov/authorities/subjects/sh85037909 Attracteurs (Mathématiques) Équations différentielles paraboliques. MATHEMATICS Topology. bisacsh Attractors (Mathematics) fast Differential equations, Parabolic fast Parabolische differentiaalvergelijkingen. gtt Dynamische systemen. gtt Attracteurs (Mathématiques) ram Equations différentielles paraboliques. ram |
| topic_facet | Attractors (Mathematics) Differential equations, Parabolic. Attracteurs (Mathématiques) Équations différentielles paraboliques. MATHEMATICS Topology. Differential equations, Parabolic Parabolische differentiaalvergelijkingen. Dynamische systemen. Equations différentielles paraboliques. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552516 |
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