In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the Cauchy problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined with the energy estimates, we obtain the pointwise estimates of the solution. keywords: semilinear dissipative wave equation, pointwise estimates, Green function. MSC...

Given two Banach function spaces we study the pointwise product space E · F , especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E ·M(E,F ) = F , where M(E,F ) denotes the space of multiplication operators from E into F .

We prove local and pointwise error estimates for the local discontinuous Galerkin method applied to the Stokes problem in two and three dimensions. By using techniques originally developed by A. Schatz [Math. Comp., 67 (1998), 877-899] to prove pointwise estimates for the Laplace equation, we prove optimal weighted pointwise estimates for both the velocity and the pressure for domains with smoo...

We prove local and pointwise error estimates for the local discontinuous Galerkin method applied to Stokes problem in two and three dimensions. By using techniques originally developed by A. Schatz [Math. Comp., 67 (1998), 877-899] to prove pointwise estimates for the Laplace equation, we prove optimal weighted pointwise estimates for both the velocity and the pressure for domains with smooth b...