Well-posedness of one-phase Stefan problems for sublinear heat equations (Q698861)

The main result of this paper is the global existence and uniqueness of the solution of the following problem: \[ u_t=u_{xx}+u^{1+\alpha}, \quad 0<t<T, \;0<x<l(t), \] \[ u(0,x)=u_0(x), \quad 0<x<l_0,\;l(0)=l_0, \qquad u(t,0)=0, \quad 0<t<T, \] \[ u(t,l(t))=0, \quad l'(t)=-u_x(t,l(t)), \quad 0<t<T, \] where \(-1<\alpha<0\) is a given constant and \(u_0\) is a given nonnegative function.