On the blow-up of solutions of a periodic nonlinear dispersive wave equation in compressible elastic rods.

DOI10.1016/j.jmaa.2003.08.006zbMath1058.35170OpenAlexW2014824189MaRDI QIDQ1421188

Zhaoyang Yin

Publication date: 26 January 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2003.08.006

zbMATH Keywords

well-posednessperiodic boundary conditions

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Second-order nonlinear hyperbolic equations (35L70)

Related Items (15)

Exact traveling wave solutions and \(L^{1}\) stability for the shallow water wave model of moderate amplitude ⋮ Blow-up issues for the hyperelastic rod equation ⋮ On blow-up structures for a generalized periodic nonlinearly dispersive wave equation ⋮ On local-in-space blow-up scenarios for a weakly dissipative rotation-Camassa–Holm equation ⋮ Some properties of solutions to the periodic two-component hyperelastic-rod wave equation ⋮ Blowup phenomena for a new periodic nonlinearly dispersive wave equation ⋮ Blowup and blowup rate of solutions to a weakly dissipative periodic rod equation ⋮ Initial boundary value problems for nonlinear dispersive wave equations ⋮ The existence of global weak solutions to the shallow water wave model with moderate amplitude ⋮ An energy-conserving Galerkin scheme for a class of nonlinear dispersive equations ⋮ Blow-up of solutions to a novel two-component rod system ⋮ On a Periodic 2-Component Camassa–Holm Equation with Vorticity ⋮ Optimal solution for the viscous nonlinear dispersive wave equation ⋮ Global existence and blow-up phenomena for a weakly dissipative periodic 2-component Camassa-Holm system ⋮ Blow-up criteria of solutions for a modified two-component hyperelastic rod system

Cites Work

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• A shallow water equation on the circle
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• Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
• Model equations for long waves in nonlinear dispersive systems

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