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The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations.
・ISBN 978-1-107-47739-1 paper GB£ 57.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-316-15103-7
| 著者・編者 | Meyer, J. C. / Needham, D. J., |
|---|---|
| シリーズ | London Mathematical Society Lecture Note Series |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2015 |
| ページ数 | 173 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-3142＞ |
解説
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 Hoelder 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.