On regularization of initial data of the modified Stefan problem (Q1909794)

Conditions of solvability and stability of the system \[ {\partial\over \partial t} (\theta+ \varphi)= \Delta\theta,\quad t\in (0, T),\quad \varepsilon^2 \kappa_1 {\partial\varphi\over \partial t}= \varepsilon^2 \Delta \varphi+ \varphi(1- \varphi^2)+ \varepsilon \kappa_2 \theta,\tag{1} \] \[ \theta|_\Sigma= g(x, t)|_\Sigma,\quad \varphi|_\Sigma= 1,\quad \theta|_{t= 0}= \theta_0(x, \varepsilon),\quad \varphi|_{t= 0}= \varphi_0(x, \varepsilon) \] are deduced. System (1) is a regularized Stefan problem.