A semidiscretization scheme for a phase-field type model for solidification

Cristina Vaz and José Luiz Boldrini

Abstract: A mathematical analysis of a time discretization scheme for an initial-boundary value problem for a phase-field type model for phase transitions is presented. Convergence of the solutions of the proposed discretized scheme is proved and existence and regularity results for the original problem are derived. The long time behavior of the constructed solutions is also considered.

Keywords: phase-field; phase transitions; semidiscretization; convergence; asymptotic behavior.

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