On weak solutions to a shallow water wave model of moderate amplitude

Abstract

The existence of global weak solutions for a dissipative model equation for shallow water wave of moderate amplitude is studied in the space C([0, ∞) x R ∩ L ∞((0, ∞); H1 R)) without the sign condition on the initial value by employing the limit technique of viscous approximation. A new one-sided lower bound and the higher integrability estimate act a key role in our analysis. Our results partly extend the work of Coclite et al. on the existence of global weak solutions to the generalized hyperlastic-rod equation.