RT Journal Article
T1 Global stability and bounds for coarsening rates within the mean-field theory for domain coarsening
A1 López Velázquez, Juan José
A1 Niethammer, B.
AB We investigate the long-time behavior of solutions to the classical mean-field model for coarsening by Lifshitz-Slyozov and Wagner (LSW). In the original work (Lifshitz and Slyozov, 1961; Wagner 1961) convergence of solutions to a uniquely determined self-similar solution was predicted. However, it is by now well known (Giron et al., 1998; Niethammer and Pego 1999, 2001) that the long-time behavior of solutions depends sensitively on the initial data. In Niethammer and Pego (1999, 2001) a necessary criterion for convergence to any self-similar solution which behaves like a finite power at the end of its (compact) support is given. It says that the data have to be regularly varying at the end of their support with the same power. This criterion is also shown to be sufficient if the power is sufficiently small and fordata which are close to self-similar.   In this article we extend the local stability result to the whole range of self-similar solutions with compact support. Our first main result establishes global stability of self-similar solutions with not too large power. The proof relies on a global contraction argument for the spreading of characteristics. In addition, we also establish upper and lower bounds for the coarsening rates of the system for a suitable class of initial data whose variation is bounded at the end of the support but not necessarily regular.
PB Taylor & Francis
SN 0360-5302
YR 2006
FD 2006
LK https://hdl.handle.net/20.500.14352/49623
UL https://hdl.handle.net/20.500.14352/49623
LA eng
NO DGES
NO DFG-Priority research program
DS Docta Complutense
RD 29 abr 2024