On the problem associated with the linear peridynamic model
- Authors: Yuldasheva A.V.1
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Affiliations:
- Филиал Московского государственнного университета им. М. В. Ломоносова в г. Ташкенте
- Issue: Vol 226 (2023)
- Pages: 170-174
- Section: Articles
- URL: https://journals.rcsi.science/2782-4438/article/view/262055
- DOI: https://doi.org/10.36535/0233-6723-2023-226-170-174
- ID: 262055
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Abstract
The uniqueness and existence of a solution to the Cauchy problem for an integro-differential equation associated with a linear peridynamic model in the mechanics of a rigid body with nonlinear elastic properties are proved.
About the authors
A. V. Yuldasheva
Филиал Московского государственнного университета им. М. В. Ломоносова в г. Ташкенте
Author for correspondence.
Email: yuasv86@mail.ru
Uzbekistan, Ташкент
References
- Алимов Ш. А., Юлдашева А. В. О разрешимости перидинамического уравнения с сингулярным ядром// Диффер. уравн. — 2021. — 57, № 3. — С. 375–386.
- Alimov Sh. A., Sheraliev Sh. On the solvability of the singular equation of peridynamics// Compl. Var. Ellipt. Equations. — 2019. — 5, № 64. — P. 873–887.
- Silling S. A. Reformulation of elasticity theory for discontinuities and long-range forces// J. Mech. Phys. Solids. — 2000. — 48, № 1. — P. 175–209.
- Titchmarsh E. C. Eigenfunction Expansions Associated with Second-Order Differential Equations. — Oxford: at the Clarendon Press, 1958.
- Yuldasheva A. V. The linear peridynamic model in elasticity theory// Lobachevskii J. Math. — 2020. — 41, № 1. — P. 137–141.
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