Blow-up analysis for the generalized hyperelastic rod equation

2025/09/19 by Yang, Shaojie
#35B44 #35L05 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.15960

Abstract

We investigate the blow-up for the generalized hyperelastic rod equation, which includes the Camassa-Holm equation, the the hyperelastic-rod wave equation, and the rotation-Camassa-Holm equation as special cases. We establish a new local-in-space blow-up criterion under certain initial data. Our local-in-space blow-up condition on the initial data is purely local in the space variable.

Citations

• On permanent and breaking waves in hyperelastic rods and rings
• Global Conservative Solutions of the Camassa–Holm Equation
• Persistence Properties and Unique Continuation of solutions of the Camassa-Holm equation
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Wave breaking for nonlinear nonlocal shallow water equations
• Symplectic structures, their Bäcklund transformations and hereditary symmetries

Related

• On permanent and breaking waves in hyperelastic rods and rings
• The local criteria for blowup of the Dullin-Gottwald-Holm equation and\n the two-component Dullin-Gottwald-Holm system
• Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation
• Blow-up phenomena for the rotation-two-component Camassa-Holm system
• Exploring the dynamics of shallow water waves and nonlinear wave propagation in hyperelastic rods: Analytical insights into the Camassa–Holm equation