The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations /
Meyer, J. C.
The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations / J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham. - Cambridge : Cambridge University Press, 2015. - 1 online resource (vii, 167 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 419 . - London Mathematical Society lecture note series ; 419. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
9781316151037 (ebook)
Cauchy problem.
Differential equations, Partial.
Differential equations, Parabolic.
QA377 / .M494 2015
515/.3534
The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations / J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham. - Cambridge : Cambridge University Press, 2015. - 1 online resource (vii, 167 pages) : digital, PDF file(s). - London Mathematical Society lecture note series ; 419 . - London Mathematical Society lecture note series ; 419. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
9781316151037 (ebook)
Cauchy problem.
Differential equations, Partial.
Differential equations, Parabolic.
QA377 / .M494 2015
515/.3534