The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations:
Reaction-diffusion theory is a topic which has developed rapidly over the last thirty years, particularly with regards to applications in chemistry and life sciences. Of particular importance is the analysis of semi-linear parabolic PDEs. This monograph provides a general approach to the study of se...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2015
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| Schriftenreihe: | London Mathematical Society lecture note series
419 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Reaction-diffusion theory is a topic which has developed rapidly over the last thirty years, particularly with regards to applications in chemistry and life sciences. Of particular importance is the analysis of semi-linear parabolic PDEs. This monograph provides a general approach to the study of semi-linear parabolic equations when the nonlinearity, while failing to be Lipschitz continuous, is Hölder and/or upper Lipschitz continuous, a scenario that is not well studied, despite occurring often in models. The text presents new existence, uniqueness and continuous dependence results, leading to global and uniformly global well-posedness results (in the sense of Hadamard). Extensions of classical maximum/minimum principles, comparison theorems and derivative (Schauder-type) estimates are developed and employed. Detailed specific applications are presented in the later stages of the monograph. Requiring only a solid background in real analysis, this book is suitable for researchers in all areas of study involving semi-linear parabolic PDEs |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (vii, 167 pages) |
| ISBN: | 9781316151037 |
| DOI: | 10.1017/CBO9781316151037 |
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Datensatz im Suchindex
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| id | DE-604.BV043940314 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:13Z |
| institution | BVB |
| isbn | 9781316151037 |
| language | English |
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| physical | 1 online resource (vii, 167 pages) |
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| publishDate | 2015 |
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| publisher | Cambridge University Press |
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| series2 | London Mathematical Society lecture note series |
| spelling | Meyer, J. C. Verfasser aut The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham Cambridge Cambridge University Press 2015 1 online resource (vii, 167 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 419 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Reaction-diffusion theory is a topic which has developed rapidly over the last thirty years, particularly with regards to applications in chemistry and life sciences. Of particular importance is the analysis of semi-linear parabolic PDEs. This monograph provides a general approach to the study of semi-linear parabolic equations when the nonlinearity, while failing to be Lipschitz continuous, is Hölder and/or upper Lipschitz continuous, a scenario that is not well studied, despite occurring often in models. The text presents new existence, uniqueness and continuous dependence results, leading to global and uniformly global well-posedness results (in the sense of Hadamard). Extensions of classical maximum/minimum principles, comparison theorems and derivative (Schauder-type) estimates are developed and employed. Detailed specific applications are presented in the later stages of the monograph. Requiring only a solid background in real analysis, this book is suitable for researchers in all areas of study involving semi-linear parabolic PDEs Cauchy problem Differential equations, Partial Differential equations, Parabolic Needham, D. J. Sonstige oth Erscheint auch als Druckausgabe 978-1-107-47739-1 https://doi.org/10.1017/CBO9781316151037 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Meyer, J. C. The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations Cauchy problem Differential equations, Partial Differential equations, Parabolic |
| title | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations |
| title_auth | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations |
| title_exact_search | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations |
| title_full | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham |
| title_fullStr | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham |
| title_full_unstemmed | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham |
| title_short | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations |
| title_sort | the cauchy problem for non lipschitz semi linear parabolic partial differential equations |
| topic | Cauchy problem Differential equations, Partial Differential equations, Parabolic |
| topic_facet | Cauchy problem Differential equations, Partial Differential equations, Parabolic |
| url | https://doi.org/10.1017/CBO9781316151037 |
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