ON THE POINTWISE DECAY ESTIMATE FOR THE WAVE EQUATION WITH COMPACTLY SUPPORTED FORCING TERM

In this paper we derive a new type of pointwise decay estimates for solutions to the Cauchy problem for the wave equation in 2D, in the sense that one can diminish the weight in the time variable for the forcing term if it is compactly supported in the spatial variables. As an application of the estimate, we also establish an improved decay estimate for the solution to the exterior problem in 2D

MODIFICATION OF THE VECTOR-FIELD METHOD RELATED TO QUADARTICALLY PERTURBED WAVE EQUATIONS IN TWO SPACE DIMENSIONS

The purpose of this paper is to shed light on the fact that the global solvability for the quadratically perturbed wave equation with small initial data in two space dimension can be shown by using only a restricted set of vector fields associated with the space-time translation and spatial rotations. As a by-product, we establish almost best possible decay estimates related to the above vector fields, as well as the tangential derivatives to the forward light cones

A Remark on Long Range Effect for a System of Semilinear Wave Equations

In this paper we consider the Cauchy problem for a system of semilinear wave equations whose nonlinearity has long range effect on the solution. Such a result was obtained by Kubo, Kubota, and Sunagawa (Math. Ann. 335 (2006)) under the assumption that the initial data are radially symmetric. The aim of this paper is to remove the radial symmetricity of the initial data for typical cases of the nonlinearities