Abstract
This paper considers the problem of determining a solution of the parabolic equation and the boundary of the two-dimensional region in which a solution of the equation is sought in the case where on the free boundary the value of the desired function and the additional condition are satisfied. For this problem a theorem asserting the existence of a smooth solution on a small time interval is proved. If is the heat equation, then the solution exists on any time interval, and it is unique.Bibliography: 7 titles.
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