Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II: applications
Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
Springer
[2021]
|
| Schriftenreihe: | SpringerBriefs in mathematics
|
| Schlagworte: | |
| Zusammenfassung: | Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed |
| Beschreibung: | ix, 128 Seiten |
| ISBN: | 9789811626623 |
Internformat
MARC
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| 264 | 1 | |a Singapore |b Springer |c [2021] | |
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| 490 | 0 | |a SpringerBriefs in mathematics | |
| 520 | 3 | |a Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model | |
| 520 | 3 | |a This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed | |
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Datensatz im Suchindex
| _version_ | 1804182894670774272 |
|---|---|
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| any_adam_object | |
| any_adam_object_boolean | |
| author | Yagi, Atsushi 1951- |
| author_GND | (DE-588)14027247X |
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| author_sort | Yagi, Atsushi 1951- |
| author_variant | a y ay |
| building | Verbundindex |
| bvnumber | BV047565475 |
| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)1286869732 (DE-599)BVBBV047565475 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV047565475 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:28:28Z |
| indexdate | 2024-07-10T09:14:48Z |
| institution | BVB |
| isbn | 9789811626623 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032940833 |
| oclc_num | 1286869732 |
| open_access_boolean | |
| owner | DE-384 |
| owner_facet | DE-384 |
| physical | ix, 128 Seiten |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Springer |
| record_format | marc |
| series2 | SpringerBriefs in mathematics |
| spelling | Yagi, Atsushi 1951- Verfasser (DE-588)14027247X aut Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications Atsushi Yagi Singapore Springer [2021] ix, 128 Seiten txt rdacontent n rdamedia nc rdacarrier SpringerBriefs in mathematics Preliminaries -- Review of Abstract Results -- Parabolic Equations -- Epitaxial Growth Model -- Chemotaxis Model This second volume continues the study on asymptotic convergence of global solutions of parabolic equations to stationary solutions by utilizing the theory of abstract parabolic evolution equations and the Łojasiewicz–Simon gradient inequality. In the first volume of the same title, after setting the abstract frameworks of arguments, a general convergence theorem was proved under the four structural assumptions of critical condition, Lyapunov function, angle condition, and gradient inequality. In this volume, with those abstract results reviewed briefly, their applications to concrete parabolic equations are described. Chapter 3 presents a discussion of semilinear parabolic equations of second order in general n-dimensional spaces, and Chapter 4 is devoted to treating epitaxial growth equations of fourth order, which incorporate general roughening functions. In Chapter 5 consideration is given to the Keller–Segel equations in one-, two-, and three-dimensional spaces. Some of these results had already been obtained and published by the author in collaboration with his colleagues. However, by means of the abstract theory described in the first volume, those results can be extended much more. Readers of this monograph should have a standard-level knowledge of functional analysis and of function spaces. Familiarity with functional analytic methods for partial differential equations is also assumed Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Mathematical analysis Analysis (Mathematics) Functional analysis Measure theory Parabolische Differentialgleichung (DE-588)4173245-5 s Evolutionsgleichung (DE-588)4129061-6 s DE-604 Erscheint auch als Online-Ausgabe, eBook 978-981-16-2663-0 |
| spellingShingle | Yagi, Atsushi 1951- Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications Evolutionsgleichung (DE-588)4129061-6 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4129061-6 (DE-588)4173245-5 |
| title | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications |
| title_auth | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications |
| title_exact_search | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications |
| title_exact_search_txtP | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications |
| title_full | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications Atsushi Yagi |
| title_fullStr | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications Atsushi Yagi |
| title_full_unstemmed | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II applications Atsushi Yagi |
| title_short | Abstract parabolic evolution equations and Łojasiewicz–Simon inequality II |
| title_sort | abstract parabolic evolution equations and lojasiewicz simon inequality ii applications |
| title_sub | applications |
| topic | Evolutionsgleichung (DE-588)4129061-6 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Evolutionsgleichung Parabolische Differentialgleichung |
| work_keys_str_mv | AT yagiatsushi abstractparabolicevolutionequationsandłojasiewiczsimoninequalityiiapplications |