Stefan problem with convection

This paper deals with the equation @?"1H(u)+@?[v->H(u)-@?u]=f in D^'(@W"T), where @W is a bounded domain in R^n(n>=2) with @?@W@?C^2, and @W"T=@Wx(0,T).H is a maximal monotone graph and v->:@W"T->R^n is a known smooth vector function. We prove the existence of weak solution, uniqueness and get an error estimate for approximating process.