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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{EJMCA_2019_7_2_a0,
     author = {U. D. Durdiev},
     title = {A problem of identification of a special {2D} memory kernel in an integro{\textendash}differential hyperbolic equation},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {4--19},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a0/}
}
TY  - JOUR
AU  - U. D. Durdiev
TI  - A problem of identification of a special 2D memory kernel in an integro–differential hyperbolic equation
JO  - Eurasian journal of mathematical and computer applications
PY  - 2019
SP  - 4
EP  - 19
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a0/
LA  - en
ID  - EJMCA_2019_7_2_a0
ER  - 
%0 Journal Article
%A U. D. Durdiev
%T A problem of identification of a special 2D memory kernel in an integro–differential hyperbolic equation
%J Eurasian journal of mathematical and computer applications
%D 2019
%P 4-19
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJMCA_2019_7_2_a0/
%G en
%F EJMCA_2019_7_2_a0
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/