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- DescriptionReaction-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 mograph provides a general approach to the study of semi-linear parabolic equations when the nlinearity, while failing to be Lipschitz continuous, is Holder and/or upper Lipschitz continuous, a scenario that is t 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 mograph. Requiring only a solid background in real analysis, this book is suitable for researchers in all areas of study involving semi-linear parabolic PDEs.
- Author BiographyJ. C. Meyer is University Fellow in the School of Mathematics at the University of Birmingham, UK. His research interests are in reaction-diffusion theory. D. J. Needham is Professor of Applied Mathematics at the University of Birmingham, UK. His research areas are applied analysis, reaction-diffusion theory and nonlinear waves in fluids. He has published over 100 papers in high-ranking journals of applied mathematics, receiving over 2000 citations.
- Author(s)D. J. Needham,J. C. Meyer
- PublisherCambridge University Press
- Date of Publication01/10/2015
- Series TitleLondon Mathematical Society Lecture Note Series
- Series Part/Volume Number419
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Weight260 g
- Width152 mm
- Height228 mm
- Spine10 mm
- Format DetailsTrade paperback (US)
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