Regularity and uniqueness results for a phase change problem in binary alloys

Jean-Francois Scheid (1, 2) , Giulio Schimperna (3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy
3 UNIPV - Dipartimento di Matematica “Felice Casorati” Department of Mathematics [Univ Pavia]

An isothermal model describing the separation of the components of a binary metallic alloy is considered. A phase transition process is also assumed to occur in the solder; hence, the state of the material is described by two order parameters, i.e., the concentration c of the first component and the phase field φ. Existence of a solution to the related initial and boundary value problem has been proved in a former paper, where, anyway, uniqueness was obtained only in a very special case. Here some further regularity and uniqueness results are shown in a more general setting using an a priori estimates – compactness argument. A key point of the proofs is the analysis of the fine continuity properties of the inverse map of the solution-dependent elliptic operator characterizing one of the equations of the system.

Mots clés: phase separation; fourth order parabolic system; solution-dependent elliptic operator; constraint; variational formulation

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Francois Scheid, Giulio Schimperna. Regularity and uniqueness results for a phase change problem in binary alloys. 4th European Conference Elliptic and Parabolic Problems, Sep 2001, Gaeta, Italy. pp.475-484, ⟨10.1142/9789812777201_0045⟩. ⟨hal-03116903⟩