Reaction-diffusion theory is a rapidly developing topic with important applications. This monograph, which includes significant new results, provides a general approach to the study of semi-linear parabolic equations with Hölder and/or upper Lipschitz continuous nonlinearities, a scenario that occurs often in reaction-diffusion models in chemical kinetics, biochemical systems and population dynamics.
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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.
J. 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.
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.Über den AutorJ. C. Meyer is University Fellow in the School of Mathemati. Nº de ref. del artículo: 31725214
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