The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations

The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations

by D. J. Needham and J. C. Meyer
Epub (Kobo), Epub (Adobe)
Publication Date: 10/11/2015

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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.

ISBN:
9781316290484
9781316290484
Category:
Differential calculus & equations
Format:
Epub (Kobo), Epub (Adobe)
Publication Date:
10-11-2015
Language:
English
Publisher:
Cambridge University Press

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