Abstract:
In this paper the author proves a theorem on the existence of a classical solution of the Stefan problem for the equation
$$
D_t\theta=\sum^n_{i,j=1}D_i[a_{ij}(x,t,\theta)D_j\theta]+f(x,t,\theta,D\theta)
$$
on a small time interval.
The solution is obtained as a limit as $\varepsilon\to0$ of solutions of auxiliary “regularized” problems. Estimates for solutions of the auxiliary problems are established that do not depend on $\varepsilon$. These estimates permit one to say something about the compactness of the family of solutions in the space $C^{2,1}$.
Bibliography: 13 titles.
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