Global attractors in abstract parabolic problems:
The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asympto...
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|---|---|
| Format: | Electronic Conference Proceeding eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2000
|
| Series: | London Mathematical Society lecture note series
278 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xii, 235 pages) |
| ISBN: | 9780511526404 |
| DOI: | 10.1017/CBO9780511526404 |
Staff View
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| 505 | 8 | |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 -- | |
| 505 | 8 | |a 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 -- | |
| 505 | 8 | |a 9.4. Comparison of X[superscript [alpha]] solution with other types of solutions -- 9.5. Final remarks | |
| 520 | |a The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field | ||
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Record in the Search Index
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| any_adam_object | |
| author | Cholewa, Jan W. |
| author_facet | Cholewa, Jan W. |
| author_role | aut |
| author_sort | Cholewa, Jan W. |
| author_variant | j w c jw jwc |
| building | Verbundindex |
| bvnumber | BV043941575 |
| classification_rvk | SI 320 SK 560 |
| collection | ZDB-20-CBO |
| 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 | (ZDB-20-CBO)CR9780511526404 (OCoLC)849887520 (DE-599)BVBBV043941575 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511526404 |
| format | Electronic Conference Proceeding eBook |
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| id | DE-604.BV043941575 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511526404 |
| language | English |
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| physical | 1 online resource (xii, 235 pages) |
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| publishDate | 2000 |
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| publisher | Cambridge University Press |
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| series2 | London Mathematical Society lecture note series |
| spelling | Cholewa, Jan W. Verfasser aut Global attractors in abstract parabolic problems Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee Cambridge Cambridge University Press 2000 1 online resource (xii, 235 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 278 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field Attractors (Mathematics) Differential equations, Parabolic Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Attraktor (DE-588)4140563-8 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Attraktor (DE-588)4140563-8 s Parabolische Differentialgleichung (DE-588)4173245-5 s Dissipatives System (DE-588)4209641-8 s Dynamisches System (DE-588)4013396-5 s 1\p DE-604 Dlotko, Tomasz Sonstige oth Chafee, Nathaniel Sonstige oth London Mathematical Society issuing body Sonstige oth Erscheint auch als Druckausgabe 978-0-521-79424-4 https://doi.org/10.1017/CBO9780511526404 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cholewa, Jan W. Global attractors in abstract parabolic problems 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) Differential equations, Parabolic Parabolische Differentialgleichung (DE-588)4173245-5 gnd Attraktor (DE-588)4140563-8 gnd Dissipatives System (DE-588)4209641-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4173245-5 (DE-588)4140563-8 (DE-588)4209641-8 (DE-588)4013396-5 |
| 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) Differential equations, Parabolic Parabolische Differentialgleichung (DE-588)4173245-5 gnd Attraktor (DE-588)4140563-8 gnd Dissipatives System (DE-588)4209641-8 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Attractors (Mathematics) Differential equations, Parabolic Parabolische Differentialgleichung Attraktor Dissipatives System Dynamisches System |
| url | https://doi.org/10.1017/CBO9780511526404 |
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