A stefan problem on a region and its boundary

Abstract

This paper considers a system of equations consisting of a nonlinear evolution equation on an open set Ωin coupled to another nonlinear evolution equation on the boundary GΩ. Rather general assumptions are made concerning the operators involved and the coupling between the two problems. Existence and uniqueness are demonstrated via a semigroup of nonlinear operators on L¹(Ω)XL¹(GΩ).

Keywords:

• Stefan problem
• dynamic boundary conditions
• Laplace-Beltrami operator,
• , non-linear semigroups