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Asymptotic behavior of the solution to the non-isothermal phase field equation
Authors:Akio Ito  Takashi Suzuki
Institution:1. Department of Electronic Engineering and Computer Science, School of Engineering, Kinki University, 1 Takayaumenobe, Higashihiroshimashi, Hiroshima 739-2116, Japan;2. Division of Mathematical Science, Department of System Innovation, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho, Toyonakashi, Osaka 560-8531, Japan
Abstract:We consider the Penrose–Fife phase field model Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43 (1990) 44–62] with homogeneous Neumann boundary condition to the nonlinear heat flux q=∇(1/θ)q=(1/θ), i.e., q=0q=0 on the boundary, where θ>0θ>0 is the temperature. There is a unique H1H1 solution globally in time with the non-empty, connected, compact ωω-limit set composed of stationary solutions, and the linearized stable stationary solution is dynamically stable.
Keywords:35K45  35K55  37L15
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