On decay properties of solutions for degenerate strongly damped wave equations of Kirchhoff type

We consider the initial-boundary value problem for the degenerate strongly damped wave equations of Kirchhoff type: . For all t⩾0, we will give the optimal decay estimate C−1(1+t)−1/γ⩽‖A1/2u(t)‖2⩽C(1+t)−1/γ, when either the coefficient ρ is appropriately small or the initial data are appropriately small. And, we will show a decay property of the norm ‖Au(t)‖2 for t⩾0.