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Global conservative solutions of the hyperelastic rod equation. (English) Zbl 1155.35301

Summary: A new approach to the analysis of wave-breaking solutions to the hyperelastic rod equation is presented in this paper. Introduction of a set of variables allows solving the singularities. A continuous semigroup of solutions is also built. The solutions have constant \(H^{1}\) energy almost every time with respect to the Lebesgue measure.

MSC:

35A21 Singularity in context of PDEs
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74J30 Nonlinear waves in solid mechanics
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