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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2017 Volume 14, Pages 1108–1119 (Mi semr851)

This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

The problem of determining the coefficient of thermal expansion of the equation of thermoviscoelasticity

Zh. D. Totievaab

a North Ossetian State University, ul. Vatutina, 46, 362025, Vladikavkaz, Russia
b Southern Mathematical Institute of Vladikavkaz Scientific Centre of Russian Academy of Sciences, ul. Markova, 93a, 362002, Vladikavkaz, Russia

Abstract: We consider the problem of finding the thermal expansion coefficient $\alpha(z),\ z\in [0,Z],$ occurring in the system of integro-differential termoviscoelasticity equations. The medium density and the Lame parameters are assumed to be function of one variable. The integrand $h(t),\ t\in [0; T]$ is known. The inverse problem is replaced by the equivalent integral equation for unknown functions. The theorem of unique solvability is proved and the stability estimate of solving the inverse problem is obtained.

Keywords: inverse problem, integro-differential equations, stability, thermal expansion coefficient, kernel.

UDC: 517.958

MSC: 35L20,35R30,35Q99

Received July 7, 2017, published November 9, 2017

DOI: 10.17377/semi.2017.14.094



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