Electron. J. Differential Equations, Vol. 2018 (2018), No. 77, pp. 1-17.

Inverse problem for a two-dimensional strongly degenerate heat equation

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
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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