Stefan problem with convection1

摘要

This paper deals with the equation ∂1H(u)+∇[v→H(u)−∇u]=f in D′(ΩT), where Ω is a bounded domain in Rn(n⩾2) with ∂Ω∈C2, and ΩT=Ω×(0,T). H is a maximal monotone graph and v→:ΩT→Rn is a known smooth vector function. We prove the existence of weak solution, uniqueness and get an error estimate for approximating process.