Decay estimates of solutions to the IBq equation

ýIn this paper we focus on the Cauchy problem for the generalizedý ýIBq equation with damped term in n -dimensional spaceý. ýWe establish the global existence and decay estimates of solution with L q (1≤q≤2) initial valueý, ýprovided that the initial value is suitably smallý. ýMoreoverý, ýwe also show that the solution is asymptotic to the solution u L to the corresponding linear equation as time tends to infinityý. ýFinallyý, ýasymptotic profile of the solution u L to the linearized problem is also discussedý.