The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations (London Mathematical Society Lecture Note Series, Series Number 419) - Softcover

Meyer, J. C.; Needham, D. J.

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

Book Description

Reaction-diffusion theory is a rapidly developing topic with important applications. This monograph, which includes significant new results, provides a general approach to the study of semi-linear parabolic equations with Hölder and/or upper Lipschitz continuous nonlinearities, a scenario that occurs often in reaction-diffusion models in chemical kinetics, biochemical systems and population dynamics.

About the Author

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.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2015
• ISBN 10: 1107477395
• ISBN 13: 9781107477391
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 173