Cauchy Problem for the One-Dimensional Equation of Motion in a Metamaterial

Propagation of nonlinear longitudinal elastic waves in a metamaterial (gradient-elastic medium) is modeled using a nonlinear Sobolev-type differential equation, for which the Cauchy problem in the space of continuous functions is investigated. Conditions for the existence of a global solution and for solution blow-up on a finite time interval are considered.

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Publication Details

Journal
Computational Mathematics and Mathematical Physics
Published
2025-03-01
DOI
https://doi.org/10.1134/s0965542524702142
Primary Topic
Nonlinear Waves and Solitons
Type
article
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article

Cauchy Problem for the One-Dimensional Equation of Motion in a Metamaterial

Х. Г. Умаров
Computational Mathematics and Mathematical Physics
Nonlinear Waves and Solitons
article

Cauchy Problem for the One-Dimensional Equation of Motion in a Metamaterial

Х. Г. Умаров
article en

Abstract

Propagation of nonlinear longitudinal elastic waves in a metamaterial (gradient-elastic medium) is modeled using a nonlinear Sobolev-type differential equation, for which the Cauchy problem in the space of continuous functions is investigated. Conditions for the existence of a global solution and for solution blow-up on a finite time interval are considered.

Computational Mathematics and Mathematical PhysicsVol. 65(3)
Chechen State University (RU), Chechen State Pedagogical Institute (RU)
Openalex Percentile: Top 93%
Nonlinear Waves and Solitons
DOISourceOpenAlex
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Cauchy Problem for the One-Dimensional Equation of Motion in a Metamaterial — Х. Г. Умаров · Computational Mathematics and Mathematical Physics (2025) | TGRS Research Map | TGRS