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

J. C. Meyer, D. J. Needham

ISBN 10: 1107477395 / ISBN 13: 9781107477391

Edité par Cambridge University Press, GB, 2015

A propos de cet article

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.

N° de réf. du vendeur LU-9781107477391

Détails bibliographiques

• Titre: The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations
• Éditeur: Cambridge University Press, GB
• Date de parution: 2015
• Langue: anglais
• ISBN à 10 chiffres: 1107477395
• ISBN à 13 chiffres: 9781107477391
• Reliure: Paperback
• État de l'article: New
• Dimensions: 15,19 L x 1,12 H x 22,81 P (centimètres) 15,19 centimètres de largeur par 1,12 centimètres de hauteur par 22,81 centimètres de profondeur
• Poids: 260 grammes

A propos de ce titre

Synopsis

A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.

À propos des auteurs

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.