The cauchy problem for non-lipschitz semi-linear parabolic partial differential equations

John Meyer, David Needham

Research output: Book/ReportBook

2 Citations (Scopus)


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.
Original languageEnglish
Place of PublicationCambridge, UK
PublisherCambridge University Press
Number of pages173
ISBN (Electronic)978-1316151037
ISBN (Print)978-1107477391
Publication statusPublished - Nov 2015

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press


  • reaction-diffusion
  • Parabolic partial differential equations


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