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Asymptotic expansions of solutions to inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative

A. M. Denisov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: Two inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative are considered. The existence and uniqueness of their solutions are proved. As the small parameter tends to zero, the solutions of the inverse problems are proved to converge to solutions of inverse problems for a parabolic equation.

Key words: inverse problem, hyperbolic equation, small parameter, parabolic equation, asymptotic expansion.

UDC: 519.633.9

Received: 06.12.2012

DOI: 10.7868/S0044466913050049

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:5, 580–587

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