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

J. C. Meyer, D. J. Needham

ISBN 10: 1107477395 / ISBN 13: 9781107477391

Editore: Cambridge University Press, GB, 2015

Riguardo questo articolo

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.

Codice articolo LU-9781107477391

Dati bibliografici

• Titolo: The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations
• Editore: Cambridge University Press, GB
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 1107477395
• ISBN 13: 9781107477391
• Rilegatura: Paperback
• Condizione: New
• Dimensioni: 15,19 L x 1,12 A x 22,81 P centimetri 15,19 centimetri di larghezza per 1,12 centimetri di altezza per 22,81 centimetri di profondità
• Peso: 260 grammi

Descrizione articolo

Riassunto

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

Informazioni sugli autori

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.