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

Nonfiction, Science & Nature, Mathematics, Differential Equations, Calculus
Cover of the book The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations by J. C. Meyer, D. J. Needham, Cambridge University Press
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Author: J. C. Meyer, D. J. Needham ISBN: 9781316290484
Publisher: Cambridge University Press Publication: October 22, 2015
Imprint: Cambridge University Press Language: English
Author: J. C. Meyer, D. J. Needham
ISBN: 9781316290484
Publisher: Cambridge University Press
Publication: October 22, 2015
Imprint: Cambridge University Press
Language: English

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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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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