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

Meyer, J. C.

Softcover

ISBN 10: 1107477395 ISBN 13: 9781107477391

Publisher: Cambridge University Press, 2015

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 this title

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2015
• Language: English
• ISBN 10: 1107477395
• ISBN 13: 9781107477391
• Binding: Paperback
• Number of pages: 176