Sufficient conditions to obtain a steady-state Stefan problem with internal energy and Dirichlet and Robin boundary conditions

G.G. GARGUICHEVICH - D.A. TARZIA

MATHEMATICAE NOTAE

Univ. Nac. de Rosario

Lugar: Rosario; Año: 2006 vol. 44 p. 53 - 63

0025-553X

We consider the problem of the steady-state temperature distribution of a material submitted to an internal energy g. We assume the material is contained in a regular bounded domain D in Rn, Boundary F=F1 U F2 U F3, with a fixed positive temperature on F1 and a Robin condition for the heat flux on F2 (or Newton´s type law). We obtain monotonicity properties for the temperature and we state two different sufficient conditions in order it is of non constant sign in D, that is, we have steady state two-phase Stefan problem.We also show an example where the necessary and sufficient conditions are given.