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JOURNALS // Eurasian Journal of Mathematical and Computer Applications // Archive

Eurasian Journal of Mathematical and Computer Applications, 2019 Volume 7, Issue 2, Pages 4–19 (Mi ejmca100)

This article is cited in 1 paper

A problem of identification of a special 2D memory kernel in an integro–differential hyperbolic equation

U. D. Durdiev

Bukhara State University, Uzbekistan, 200100, 11 M. Ikbal St. Bukhara

Abstract: We consider an inverse problem for a partial integro–differential equation of the second order related to recovering a kernel (memory) in the integral term of this equation. It is supposed that the unknown kernel is a trigonometric polynomial with respect to the spatial variables with coefficients continuous with respect to the time variable. The direct problem for a hyperbolic integro–differential equation is the initial-boundary value problem for the half-space $x > 0$ with the zero initial Cauchy data and a special Neumann data at $x = 0$. Local existence theorem and stability estimates for the solution to the inverse problem are obtained.

Keywords: kernel, Neumann data, Fourier series, Heaviside step-function, Bessel function, Dirac function, integro–differential equation, Kronecker symbol.

MSC: 45E10, 45G15, 65M32

Language: English



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