Geodesic
A problem of identification of a special 2D memory kernel in an integro–differential hyperbolic equation
Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 2, pp. 4-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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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: Neumann data, Fourier series, Heaviside step-function, Bessel function, Dirac function, integro–differential equation, Kronecker symbol.
Mots-clés : kernel 
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     author = {U. D. Durdiev},
     title = {A problem of identification of a special {2D} memory kernel in an {integro{\cyrv}{\CYRDJE}{\textquotedblleft}differential} hyperbolic equation},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {4--19},
     year = {2019},
     volume = {7},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a0/}
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U. D. Durdiev. A problem of identification of a special 2D memory kernel in an integro–differential hyperbolic equation. Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 2, pp. 4-19. http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a0/