Solution blow-up and global solvability of the Cauchy problem for the equation of moderately long longitudinal waves in a viscoelastic rod

DOI10.1134/S0965542523070151zbMath1525.35048OpenAlexW4387144052MaRDI QIDQ6053563

Kh. G. Umarov

Publication date: 19 October 2023

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542523070151

zbMATH Keywords

global solutionsolution blow-upnonlinear Sobolev-type equationslongitudinal waves in viscoelastic rod

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Initial value problems for higher-order hyperbolic equations (35L30) Blow-up in context of PDEs (35B44)

Cites Work

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• Solvability conditions of the Cauchy problem for pseudohyperbolic equations
• Semigroups of operators, cosine operator functions, and linear differential equations
• The Cauchy problem for the nonlinear long longitudinal waves equation in a viscoelastic rod
• Cosine families and abstract nonlinear second order differential equations
• Blow-up of solutions of non-linear equations of Kadomtsev-Petviashvili and Zakharov-Kuznetsov types
• Model equations for long waves in nonlinear dispersive systems

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