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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 4, 2000, pp. 953–976
DOI: 10.4171/ZAA/992

Published online: 2000-12-31

Asymptotic Justification of the Conserved Phase-Field Model with Memory

Veronica Felli[1]

(1) Università degli Studi di Milano-Bicocca, Italy

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.

Keywords: Phase-field models, phase transitions, heat conduction with memory, asymptotic analysis, error estimates

Felli Veronica: Asymptotic Justification of the Conserved Phase-Field Model with Memory. Z. Anal. Anwend. 19 (2000), 953-976. doi: 10.4171/ZAA/992