On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type

We consider the initial data boundary value problem for the degenerate dissipative wave equations of Kirchhoff type ρu′′ + ∥ A 1/2 u ∥ 2γ Au + u ′ = 0. When either the coefficient ρ or the initial data are appropriately small at least, we show the global existence theorem by using suitable identities together with the energy. Moreover, under the same assumption for ρ and the initial data, we derive the sharp decay estimates of the solutions and their second derivatives. Copyright © 2011 John Wiley & Sons, Ltd.