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<p>For a&#xa0;nonlinear dispersion-dissipation Sobolev-typepartial differential equationmodeling the propagation of longitudinal strain wavesin a&#xa0;nonlinear elastic rod, the Cauchy problem is studied in the space of continuous functionsdefined on the entire real axis and having limits at infinity.Some conditions ensuring existence of a&#xa0;global solution and blow-up of a&#xa0;solution to the Cauchy problem on a&#xa0;finite time interval are exposed.</p>

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Blow-up of a Solution and Global Solvability of the Cauchy Problem for the Equation Modeling the Propagation of Longitudinal Strain Waves

  • 期刊论文

  • 发表日期：

    2025年3月23日

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  • Kh. G. Umarov

摘要

For a nonlinear dispersion-dissipation Sobolev-typepartial differential equationmodeling the propagation of longitudinal strain wavesin a nonlinear elastic rod, the Cauchy problem is studied in the space of continuous functionsdefined on the entire real axis and having limits at infinity.Some conditions ensuring existence of a global solution and blow-up of a solution to the Cauchy problem on a finite time interval are exposed.