The semigroup approach to the two-phase Stefan problem with nonlinear flux conditions. (English) Zbl 0593.35092

Magenes, A.; Verdi, C.

Free boundary problems: applications and theory, Vol. III, Proc. Int. Colloq., Maubuisson/France 1984, Res. Notes Math. 120, 28-39 (1985).

[For the entire collection see Zbl 0578.35003.]
The aim of this paper is to present some simple remarks, in particular from the numerical point of view, on the two-phase Stefan problem in several space variables, with a nonlinear flux condition on the fixed part of the boundary. The approach is based on the theory of the nonlinear contraction semigroups in \(L^ 1(\Omega)\).

MSC:

35R35	Free boundary problems for PDEs
35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
47H20	Semigroups of nonlinear operators

Keywords:

two-phase Stefan problem; nonlinear flux; nonlinear contraction semigroups

Citations:

Zbl 0578.35003