Explicit decay rates for a generalized Boussinesq–Burgers system

Abstract

This paper is concerned with the long-time asymptotic behavior of classical solutions to the Cauchy problem for the generalized Boussinesq–Burgers system: ut+(uw)x=εuxx,x∈R,t>0,wt+uγ+w22x=μwxx+δwxxt,x∈R,t>0,(u,w)(x,0)=(u0,w0)(x),x∈R,where γ≥2, ε, μ and δ are positive constants. By utilizing time-weighted energy methods, we identify the explicit decay rates of classical solutions to the Cauchy problem under mild conditions on the initial data. This generalizes the previous result obtained in Zhu and Liu (2016) by extending the exponent γ from a single value to the half real line.