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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| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2015.
|
| Series: | London Mathematical Society lecture note series ;
419. |
| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Meyer, J. C. |q (John Christopher), |e author. | |
| 245 | 1 | 4 | |a The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations / |c J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2015. | |
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 419 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015). | ||
| 520 | |a 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. | ||
| 650 | 0 | |a Cauchy problem. | |
| 650 | 0 | |a Differential equations, Partial. | |
| 650 | 0 | |a Differential equations, Parabolic. | |
| 700 | 1 | |a Needham, D. J. |q (David J.), |e author. | |
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