JournalszaaVol. 19, No. 4pp. 953–976

Asymptotic Justification of the Conserved Phase-Field Model with Memory

  • Veronica Felli

    Università degli Studi di Milano-Bicocca, Italy
Asymptotic Justification of the Conserved Phase-Field Model with Memory cover
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Abstract

We consider a conserved phase-field model with memory in which the Fourier heat conduction law is replaced by a constitutive assumption of Curtin-Pipkin type; the system is conserved in the sense that the initial mass of the order parameter is preserved during the evolution. We investigate a Cauchy-Neumann problem for this model which couples an integro-differential equation with a nonlinear fourth-order equation for the phase field. here we assume that the heat flux memory kernel has a decreasing exponential as principal part and we study the behaviour of solutions when this kernel converges to a Dirac mass. We show that the solution to the conserved phase-field model with memory converges to a solution to the phase-field problem without memory under suitable assumptions on the data.

Cite this article

Veronica Felli, Asymptotic Justification of the Conserved Phase-Field Model with Memory. Z. Anal. Anwend. 19 (2000), no. 4, pp. 953–976

DOI 10.4171/ZAA/992