TY  - BOOK
AU  - Meyer,J.C.
AU  - Needham,D.J.
TI  - The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations
T2  - London Mathematical Society lecture note series
SN  - 9781316151037 (ebook)
AV  - QA377 .M494 2015
U1  - 515/.3534 23
PY  - 2015///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Cauchy problem
KW  - Differential equations, Partial
KW  - Differential equations, Parabolic
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015)
N2  - 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
UR  - https://doi.org/10.1017/CBO9781316151037
ER  -