On the Existence of Global Weak Solutions for a Weakly Dissipative Hyperelastic Rod Wave Equation

Abstract

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