The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations /
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| Author / Creator: | Meyer, J. C. (John Christopher), author. |
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| Imprint: | Cambridge : Cambridge University Press, 2015. |
| Description: | vii, 167 pages ; 23 cm. |
| Language: | English |
| Series: | London Mathematical Society lecture note series ; 419 London Mathematical Society lecture note series ; 419. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/10488433 |
| Summary: | 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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| Physical Description: | vii, 167 pages ; 23 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781107477391 1107477395 |