The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations - 419

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.