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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Kh. G. Umarov

摘要

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.