A Two-Phase Free Boundary Problem for the Nonlinear Heat Equation
S. De Lillo, Maria Cesarina Salvatori · Journal of Nonlinear Mathematical Physics · 2004
A two-phase free boundary problem associated with nonlinear heat conduction is considered.The problem is mapped into two one-phase moving boundary problems for the linear heat equation, connected through a constraint on the relative motion of their moving boundaries.Existence and uniqueness of the solution is proved for small times and a particular exact solution is discussed.