On Global Stability for Lifschitz–Slyozov–Wagner Like Equations

This paper is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz–Slyozov–Wagner (LSW) system in the case when the initial data has compact support. The main result of the paper is a proof of weak global asymptotic s...

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Bibliographic Details
Published in:Journal of statistical physics 2014-03, Vol.154 (5), p.1251-1291
Main Authors: Conlon, Joseph G., Niethammer, Barbara
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:This paper is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz–Slyozov–Wagner (LSW) system in the case when the initial data has compact support. The main result of the paper is a proof of weak global asymptotic stability for LSW like systems. Previously strong local asymptotic stability results were obtained by Niethammer and Velázquez for the LSW system with initial data of compact support. Comparison to a quadratic model plays an important part in the proof of the main theorem when the initial data is critical. The quadratic model extends the linear model of Carr and Penrose, and has a time invariant solution which decays exponentially at the edge of its support in the same way as the infinitely differentiable self-similar solution of the LSW model.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-0927-9