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.
| ISBN: | 9781107477391 |
| Publication date: | 22nd October 2015 |
| Author: | J C University of Birmingham Meyer, D J University of Birmingham Needham |
| Publisher: | Cambridge University Press |
| Format: | Paperback |
| Pagination: | 173 pages |
| Series: | London Mathematical Society Lecture Note Series |
| Genres: |
Differential calculus and equations Integral calculus and equations Mathematical modelling |