On the existence of global weak solutions for a weakly dissipative hyperelastic rod wave equation (Q2336271)

Summary: Assuming that the initial value \(v_0(x)\) belongs to the space \(H^1(\mathbb{R})\), we prove the existence of global weak solutions for a weakly dissipative hyperelastic rod wave equation in the space \(C([0, \infty) \times \mathbb{R}) \bigcap L^\infty([0, \infty); H^1(\mathbb{R}))\). The limit of the viscous approximation for the equation is used to establish the existence.