Decay estimates of solutions to the IBq equation

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in n-dimensional space‎. ‎We establish the global existence and decay estimates of solution with Lq(1≤q≤2) initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution uL to the corresponding linear equation as time tends to infinity‎. ‎Finally‎, ‎asymptotic profile of the solution uL to the linearized problem is also discussed‎.