Finite Time Blowup in a Fourth-Order Dispersive Wave Equation with Nonlinear Damping and a Non-Local Source

Abstract

In this work, we consider a class of initial boundary value problems for fourth-order dispersive wave equations with superlinear damping and non-local source terms as well as time-dependent coefficients in Ω×(t>0), where Ω is a bounded domain in RN and N≥2. We prove that there exists a safe time interval of existence in the solution [0,T], with T being a lower bound of the blowup time t*. Moreover, we find an explicit lower bound of t*, assuming the coefficients are positive constants.