Blow-up issues for the hyperelastic rod equation

DOI10.1007/s00605-022-01715-zzbMath1514.35429OpenAlexW4280618034MaRDI QIDQ6102537

Shaojie Yang, Jianmin Zhao

Publication date: 9 May 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-022-01715-z

zbMATH Keywords

well-posednessblow-upnonlinear wavehyperelastic rod

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear waves in solid mechanics (74J30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with mechanics of deformable solids (35Q74) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Wave breaking phenomena for the generalized hyperelastic rod wave equation

Cites Work

• Unnamed Item
• On some wave breaking for the nonlinear integrable shallow water wave equations
• On the blow-up of solutions to a nonlinear dispersive rod equation
• Blow-up of solutions to the DGH equation
• Stability of a class of solitary waves in compressible elastic rods
• Wave breaking for nonlinear nonlocal shallow water equations
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• On the blow-up of solutions of a periodic nonlinear dispersive wave equation in compressible elastic rods.
• Breakdown of a shallow water equation
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Wave Breaking and Persistence Properties for the Dispersive Rod Equation
• An integrable shallow water equation with peaked solitons
• Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
• Model equations for long waves in nonlinear dispersive systems
• Local well‐posedness and blow‐up criteria of solutions for a rod equation
• Blow-up phenomenon for a periodic rod equation

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