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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations

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

Meyer, J. C.
Needham, D. J.

Paperback

Series: London Mathematical Society Lecture Note, Book 419

General Mathematics

ISBN10: 1107477395
ISBN13: 9781107477391
Publisher: Cambridge University Press
Published: Oct 22 2015
Pages: 173
Weight: 0.58
Height: 0.40 Width: 6.04 Depth: 9.02
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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