The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations / J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham.
Meyer, J. C. (John Christopher)| Call Number | 515/.3534 |
| Author | Meyer, J. C. author. |
| Title | The Cauchy problem for non-Lipschitz semi-linear parabolic partial differential equations / J.C. Meyer, University of Birmingham, D.J. Needham, University of Birmingham. |
| Physical Description | 1 online resource (vii, 167 pages) : digital, PDF file(s). |
| Series | London Mathematical Society lecture note series ; 419 |
| Notes | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Summary | 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. |
| Added Author | Needham, D. J. author. |
| Subject | CAUCHY PROBLEM. DIFFERENTIAL EQUATIONS, PARTIAL. Differential equations, Parabolic. |
| Multimedia |
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| Summary | 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. |
| Notes | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Subject | CAUCHY PROBLEM. DIFFERENTIAL EQUATIONS, PARTIAL. Differential equations, Parabolic. |
| Multimedia |