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  3. The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations
  • Cited by 2
Publisher:
Cambridge University Press
Online publication date:
August 2015
Print publication year:
2015
Online ISBN:
9781316151037
DOI:
https://doi.org/10.1017/CBO9781316151037
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Modeling and Methods
Series:
London Mathematical Society Lecture Note Series (419)
Information

Book description

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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