Lq-Decay Rates of Solutions for Benjamin–Bona–Mahony–Burgers Equations

This paper studies the asymptotic behavior of solutions for the Benjamin–Bona–Mahony–Burgers equations ut−uxxt−αuxx+βux+upux=0, x R, t 0, with the initial data ut=0=u0(x)→0 as x→±∞. Under the restrictions ∫∞−∞ u0(x) dx=0 and ∫x−∞ u0(y) dy W2p+1, 1, we obtain more results on the energy decay rates of the solutions in the forms that if p 1, then ∂jxu(t) L2=O(1) t−(2j+3)/4 for j=0, 1, …, 2p−1, and ∂jxu(t) Lq=O(1) t−((j+2) q−1)/(2q) for 2