Mykola Ivanchov, Vitaliy Vlasov
Abstract:
This article concerns the existence and uniqueness of solutions
in the problem of identifying the leading coefficient in a
two-dimensional heat equation. We suppose that unknown coefficient
depends on the time variable and the equation is strongly degenerate.
Applying Schauder fixed-point theorem, we find conditions for
existence of a classical solution.
Submitted November 29, 2017. Published March 20, 2018.
Math Subject Classifications: 35R30, 35K10, 35A09, 35A02.
Key Words: Inverse problem; strongly degenerate heat equation;
Green function; classical solution.
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Mykola Ivanchov Department of Differential Equations Ivan Franko National University of Lviv Universytetska st., 1, 79000, Ukraine email: mykola.ivanchov@lnu.edu.ua |
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Vitaliy Vlasov Department of Differential Equations Ivan Franko National University of Lviv Universytetska st., 1, 79000, Ukraine email: siphiuel@gmail.com |
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