The Cauchy Problem for NonLipschitz SemiLinear Parabolic Partial Differential Equations: 419 (London Mathematical Society Lecture Note Series, Series Number 419)

Meyer, J. C.

ISBN 10: 1107477395 / ISBN 13: 9781107477391

Published by Cambridge University Press, 2015

About this Item

A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences. Series: London Mathematical Society Lecture Note Series. Num Pages: 173 pages. BIC Classification: PBKJ; PBKL; PBWH. Category: (P) Professional & Vocational. Dimension: 228 x 152 x 10. Weight in Grams: 260. . 2015. paperback. . . . .

Seller Inventory # V9781107477391

Bibliographic Details

• Title: The Cauchy Problem for NonLipschitz SemiLinear Parabolic Partial Differential Equations: 419 (London Mathematical Society Lecture Note Series, Series Number 419)
• Publisher: Cambridge University Press
• Publication Date: 2015
• Language: English
• ISBN 10: 1107477395
• ISBN 13: 9781107477391
• Binding: Soft cover
• Condition: New

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.