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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| Format: | E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2015
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| Schriftenreihe: | London Mathematical Society lecture note series
419 |
| Online-Zugang: | Volltext |
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| 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. |
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| Beschreibung: | 1 Online-Ressource (vii, 167 Seiten) |
| ISBN: | 9781316151037 |
| DOI: | 10.1017/CBO9781316151037 |