Deduction of a generalized Stefan-problem and its solution by means of an iterative method

A. Capuano (1) , Francesco Dell'Isola (2, 3)

1 Istituto di Matematica
2 Dipartimento di Ingegneria Strutturale e Geotecnica
3 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita

A generalized Stefan-problem arise when the thermomechanical theory for continua with interface, proposed by A. Romano and others [10, 11], is used for modelling a "one -dimensional" system where a phase transition is taking place and the difference in density between the phases cannot be neglected. This problem is solved by means of an iterative method which allows for the construction of a solution in a suitable time interval. An integral representation of the moving boundary "s" is then shown, which immediately proves the uniqueness of the solution in its existence time interval. The repeated application of the iterative method allows us to construct the solution up to the instant T* only, that is up to that instant when (eventually) of the phases disappears. Proof techniques we have used sum to be convenient for numerical applications and applicable to more general problems. Next we show a global continuous-dependence-on-coefficients- and data theorem. The existence and continuous dependence theorem thus proved confirms the applicability of the proposed thermomechanical model. We finally discuss the physical meaning of the failure of quoted proof-techniques when t > T

Domaines: Mécanique [physics.med-ph]

A. Capuano, Francesco Dell'Isola. Deduction of a generalized Stefan-problem and its solution by means of an iterative method. Archives of Mechanics AMS Warsaw, 1987, pp.20. ⟨hal-00502469⟩