The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations
£51.99
Part of London Mathematical Society Lecture Note Series
- Authors:
- J. C. Meyer, University of Birmingham
- D. J. Needham, University of Birmingham
- Date Published: October 2015
- availability: Available
- format: Paperback
- isbn: 9781107477391
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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.
Read more- A novel new approach to the study of semi-linear parabolic PDEs, of interest to those working in reaction-diffusion theory and its applications
- Presents a number of specific applications in combustion, autocatalysis, biochemical reactions, epidemiology and population dynamics
- Requires only a solid appreciation of real analysis, making it suitable for a wide range of researchers in applied mathematics and the theoretical aspects of physical, chemical and biological sciences
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×Product details
- Date Published: October 2015
- format: Paperback
- isbn: 9781107477391
- length: 173 pages
- dimensions: 228 x 152 x 10 mm
- weight: 0.26kg
- availability: Available
Table of Contents
1. Introduction
2. The bounded reaction-diffusion Cauchy problem
3. Maximum principles
4. Diffusion theory
5. Convolution functions, function spaces, integral equations and equivalence lemmas
6. The bounded reaction-diffusion Cauchy problem with f e L
7. The bounded reaction-diffusion Cauchy problem with f e Lu
8. The bounded reaction-diffusion Cauchy problem with f e La
9. Application to specific problems
10. Concluding remarks.
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