Some properties of solutions to the periodic two-component hyperelastic-rod wave equation

In this paper, we study the Cauchy problem of the periodic two-component hyperelastic-rod wave equation. We first establish the local well-posedness and precise blow-up scenario. Then we obtain several blow-up results and the blowup rate of strong solutions. Moreover, we present two global existence results for strong solutions. Finally, we consider analyticity of solutions and the initial–boundary value problem.