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

A monograph containing significant new developments in the theory of reaction-diffusion systems, particularly those arising in chemistry and life sciences.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 H?lder and/or upper Lipschitz continuous nonlinearities, a scenario that occurs often in reaction-diffusion models in chemical kinetics, biochemical systems and population dynamics.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 H?lder and/or upper Lipschitz continuous nonlinearities, a scenario that occurs often in reaction-diffusion models in chemical kinetics, biochemical systems and population dynamics.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 H?lder 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 l³j