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

 
9781107477391: The Cauchy Problem for NonLipschitz SemiLinear Parabolic Partial Differential Equations: 419 (London Mathematical Society Lecture Note Series, Series Number 419)

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.

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Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Parti

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.

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  • PublisherCambridge University Press
  • Publication date2015
  • ISBN 10 1107477395
  • ISBN 13 9781107477391
  • BindingPaperback
  • LanguageEnglish
  • Number of pages176

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