Cauchy problem for the equation of longitudinal vibrations of a thick rod with allowance for transverse inertia

DOI10.1134/S0012266122010086zbMath1485.35122OpenAlexW4225621507WikidataQ114075337 ScholiaQ114075337MaRDI QIDQ2117974

Kh. G. Umarov

Publication date: 22 March 2022

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266122010086

zbMATH Keywords

equation of Sobolev typeCauchy problem in the half-plane

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) One-parameter semigroups and linear evolution equations (47D06) Vibrations in dynamical problems in solid mechanics (74H45) Initial value problems for nonlinear higher-order PDEs (35G25) Blow-up in context of PDEs (35B44)

Cites Work

• Semigroups of operators, cosine operator functions, and linear differential equations
• The equation and several problems associated with it
• Cosine families and abstract nonlinear second order differential equations
• Model equations for long waves in nonlinear dispersive systems
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