Cauchy Problem for NonLipschitz SemiLinear Parabolic Partial Diff… 9781107477391

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The Cauchy Problem for NonLipschitz SemiLinear Parabolic Partial Differential Equations: 419 (London Mathematical Society Lecture Note Series, Series Number 419)J. C. Meyer

Cambridge University PressPaperback

Unused and unread, cosmetic imperfections such as scuffs, creases or knocks. Stamped 'damaged' by publisher to a non-text page.

EAN: 9781107477391Published: 22/10/2015Language: English

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.

1. Introduction2. The bounded reaction-diffusion Cauchy problem3. Maximum principles4. Diffusion theory5. Convolution functions, function spaces, integral equations and equivalence lemmas6. The bounded reaction-diffusion Cauchy problem with f e L7. The bounded reaction-diffusion Cauchy problem with f e Lu8. The bounded reaction-diffusion Cauchy problem with f e La9. Application to specific problems10. Concluding remarks.

 

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