The pointwise estimates of solutions for semilinear dissipative wave equation in multi-dimensions

In this paper, we study the global-in-time existence and the pointwise estimates of solutions to the Cauchy problem for the dissipative wave equation in multi-dimensions. Using the fixed point theorem, we obtain the global existence of the solution. In addition, the pointwise estimates of the solution are obtained by the method of the Green function. Furthermore, we obtain the L p , 1 ⩽ p ⩽ ∞ , convergence rate of the solution.