The pointwise estimates of solutions for dissipative wave equation in multi-dimensions (Q946969)

The pointwise estimate of the solution \(u(x ,t)\) is obtained by using Green function techniques and without making any assumption regarding the space dimension. The lower, middle and higher frequency parts of the Fourier transform of the Green function are estimated by Taylor expansions, Fourier analysis and respectively by the Kirchhoff formula. Further, under certain assumptions regarding initial data, \(L^p\) decay estimates of the solution are shown.