ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35, 82 Carr, Jack , Heriot-Watt University, Edinburgh, Scotland Asymptotic Behaviour of Solutions to a simplified Lifshitz-Slyozov Equation In the theory of coarsening of dilute alloys, supersaturated solutions and mushy zones, a central role is played by a system of integro-differential equations developed by Lifshitz and Slyozov. The theory claims that all solutions approach a universal form for large values of time. For a particular case, we give a rigorous analysis of the asymptotic behaviour of solutions. The results show that a large number of possible asymptotics are possible. This is joint work with Oliver Penrose.