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

Abstract

Assuming that the initial valuev0(x)belongs to the spaceH1(R), we prove the existence of global weak solutions for a weakly dissipative hyperelastic rod wave equation in the spaceC([0,∞)×R)⋂‍L∞([0,∞);H1(R)). The limit of the viscous approximation for the equation is used to establish the existence.