TY - BOOK
T1 - The cauchy problem for non-lipschitz semi-linear parabolic partial differential equations
AU - Meyer, John
AU - Needham, David
PY - 2015/11
Y1 - 2015/11
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.
AB - 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.
KW - reaction-diffusion
KW - Parabolic partial differential equations
UR - http://www.cambridge.org/us/academic/subjects/mathematics/differential-and-integral-equations-dynamical-systems-and-co/cauchy-problem-non-lipschitz-semi-linear-parabolic-partial-differential-equations?format=PB
U2 - 10.1017/CBO9781316151037
DO - 10.1017/CBO9781316151037
M3 - Book
SN - 978-1107477391
T3 - London Mathematical Society Lecture Note Series
BT - The cauchy problem for non-lipschitz semi-linear parabolic partial differential equations
PB - Cambridge University Press
CY - Cambridge, UK
ER -