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On regularization of initial data of the modified Stefan problem. (English. Russian original) Zbl 0855.35136

Math. Notes 57, No. 5, 559-564 (1995); translation from Mat. Zametki 57, No. 5, 793-802 (1995).
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.

MSC:

35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
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