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

The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations
Author :
Publisher : Cambridge University Press
Total Pages : 177
Release :
ISBN-10 : 9781316301074
ISBN-13 : 1316301079
Rating : 4/5 (74 Downloads)

Book Synopsis The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations by : J. C. Meyer

Download or read book The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations written by J. C. Meyer and published by Cambridge University Press. This book was released on 2015-10-22 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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