Geodesic
Initial data problem for an equation related to a peridynamic model in a two-dimensional domain
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 37 (2021) no. 4, pp. 45-52 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the uniqueness and existence of a solution of Cauchy problem for an integro-differential equation associated with a peridynamic model of solid mechanics in a two-dimensional domain are proved.
Keywords: integro-differential equation, peridynamic, integral operator, Fourier method, Sobolev space. 
@article{VKAM_2021_37_4_a5,
     author = {A. V. Yuldasheva},
     title = {Initial data problem for an equation related to a peridynamic model in a two-dimensional domain},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {45--52},
     year = {2021},
     volume = {37},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a5/}
}
TY  - JOUR
AU  - A. V. Yuldasheva
TI  - Initial data problem for an equation related to a peridynamic model in a two-dimensional domain
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2021
SP  - 45
EP  - 52
VL  - 37
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a5/
LA  - ru
ID  - VKAM_2021_37_4_a5
ER  - 
%0 Journal Article
%A A. V. Yuldasheva
%T Initial data problem for an equation related to a peridynamic model in a two-dimensional domain
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2021
%P 45-52
%V 37
%N 4
%U http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a5/
%G ru
%F VKAM_2021_37_4_a5
A. V. Yuldasheva. Initial data problem for an equation related to a peridynamic model in a two-dimensional domain. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 37 (2021) no. 4, pp. 45-52. http://geodesic.mathdoc.fr/item/VKAM_2021_37_4_a5/

[1] Alimov Sh. A., Yuldasheva A. V., “O razreshimosti peridinamicheskogo uravneniya s singulyarnym yadrom”, Differentsial'nyye uravneniya, 57:3 (2021), 375-386 (In Russian) | Zbl

[2] Du Q., Kamm J. R., Lehoucq R. B., Parks Michael L., “A new approach for a nonlocal, nonlinear conservation law”, SIAM J. Appl. Math., 72:1 (2012), 464–487 | DOI | Zbl

[3] Alimov S. A., Cao Y., Ilhan O. A., “On the problems of peridynamics with special convolution kernels”, J. of Integral Equations and Applications, 26 (2014), 301-321 | DOI | Zbl

[4] Alimov S. A., Sheraliev S., “On the solvability of the singular equation of peridynamics”, Complex Variables and Elliptic Equations, 2019, no. 5, 873-887 | DOI | Zbl

[5] Yuldasheva A. V., “On Solvability of One Singular Equation of Peridynamics”, Lob. J. Math., 41:6 (2020), 1131–1136 | Zbl

[6] Nikol'skiy S. M., Approximation of functions of several variables and imbedding theorems, New York: Springer-Verlag, Grundl. Math. Wissensch, 1975, 418 pp.