Blow-up phenomena for a nonlinear shallow water wave model

Abstract

Abstract We investigate a nonlinear shallow water wave equation, which contains the Fornberg–Whitham model. The L 2 $L^{2}$ conservation law of solutions for the nonlinear equation is derived. Employing the Riccati-type differential inequalities, we give sufficient conditions such that the wave breaking of solutions happens at finite time. The wave-breaking rate and lifespan of solutions are also discussed.

Keywords

• Conservation law
• Boundedness of solutions
• Shallow water wave equations
• Wave breaking