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- W3102578808 abstract "We consider, in a $D-$dimensional cylinder, a non--local evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider sub--critical temperatures, for which there are two local spatially homogeneous equilibria, and show a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibrium; i.e., the planar fronts: We show that an initial perturbation of a front that is sufficiently small in $L^2$ norm, and sufficiently localized yields a solution that relaxes to another front, selected by a conservation law, in the $L^1$ norm at an algebraic rate that we explicitly estimate. We also obtain rates for the relaxation in the $L^2$ norm and the rate of decrease of the excess free energy." @default.
- W3102578808 created "2020-11-23" @default.
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- W3102578808 date "2012-05-01" @default.
- W3102578808 modified "2023-09-27" @default.
- W3102578808 title "STABILITY OF PLANAR FRONTS FOR A NON-LOCAL PHASE KINETICS EQUATION WITH A CONSERVATION LAW IN D ≤ 3" @default.
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- W3102578808 doi "https://doi.org/10.1142/s0129055x12500092" @default.
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