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1982•Mathematics of the USSR-SbornikRequires access

ON A PROBLEM WITH FREE BOUNDARY FOR PARABOLIC EQUATIONS

Anvarbek Meirmanov

Open publisher page 8 citations

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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What this paper is about

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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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Free boundary problem, Boundary value problem, Mixed boundary condition, Mathematical analysis, Function (biology), Mathematics, Robin boundary condition, Cauchy boundary condition

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ON A PROBLEM WITH FREE BOUNDARY FOR PARABOLIC EQUATIONS — Research Paper | ScholarLens