Abstract

The uniqueness and existence of the solution of an implicit free boundary problem for the heat equation u xx -u t =0,0≤c≤s(t),0≤t≤T u(x,0)=φ(x),0≤x≤b,u x (0,t)=f 1 (t),0≤t≤T us ( t ) , t=f 2 s ( t ) , t,u x s ( t ) , t=gs ( t ) , t,0≤t≤T are established.