The Cauchy Problem for Non-lipschitz Semi-linear Parabolic Partial Differential Equations

Meyer, J. C./ Needham, D. J.

ISBN 10: 1107477395 / ISBN 13: 9781107477391

Published by Cambridge Univ Pr, 2015

About this Item

1st edition. 173 pages. 9.00x6.00x0.50 inches. In Stock.

Seller Inventory # x-1107477395

Bibliographic Details

• Title: The Cauchy Problem for Non-lipschitz Semi-linear Parabolic Partial Differential Equations
• Publisher: Cambridge Univ Pr
• Publication Date: 2015
• Language: English
• ISBN 10: 1107477395
• ISBN 13: 9781107477391
• Binding: Paperback
• Condition: Brand New
• Weight: 0.26 kilograms

About this title

Synopsis

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.

About the Authors

J. C. Meyer is University Fellow in the School of Mathematics at the University of Birmingham, UK. His research interests are in reaction-diffusion theory.

D. J. Needham is Professor of Applied Mathematics at the University of Birmingham, UK. His research areas are applied analysis, reaction-diffusion theory and nonlinear waves in fluids. He has published over 100 papers in high-ranking journals of applied mathematics, receiving over 2000 citations.