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 HÃlder 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. Language: English