A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face
The following non-classical free boundary problem is considered \[ u_t-u_{xx}=-F(u(0,t)),\quad 0<x<s(t),\,\,\, 0<t<T, \] \[ u(x,0)=h(x),\;\;0<x<s(0),\quad u_x(0,t)=-g(t)\leq 0,\,0<t<T, \] \[ u(s(t),t)=0,\quad u_x(s(t),t)=-s'(t). \] The authors reduce this problem to a system of two Volterra integral equations and prove the existence and uniqueness of the classical solution.
scientific article; zbMATH DE number 5083735
scientific article