Self-similar solutions for the LSW model with encounters

The LSW model with encounters has been suggested by Lifshitz and Slyozov as a regularization of their classical mean-field model for domain coarsening to obtain universal self-similar long-time behavior. We rigorously establish that an exponentially decaying self-similar solution to this model exist...

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Bibliographic Details
Published in:Journal of Differential Equations 2009-10, Vol.247 (8), p.2282-2309
Main Authors: Herrmann, M., Niethammer, B., Velázquez, J.J.L.
Format: Article
Language:English
Subjects:
Coarsening with encounters
Kinetics of phase transitions
Self-similar solutions
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Summary:The LSW model with encounters has been suggested by Lifshitz and Slyozov as a regularization of their classical mean-field model for domain coarsening to obtain universal self-similar long-time behavior. We rigorously establish that an exponentially decaying self-similar solution to this model exist, and show that this solutions is isolated in a certain function space. Our proof relies on setting up a suitable fixed-point problem in an appropriate function space and careful asymptotic estimates of the solution to a corresponding homogeneous problem.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2009.07.021