Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 150, pp. 1-12.
Title: Dispersive estimates for a linear wave equation with
electromagnetic potential
Author: Davide Catania (Univ. di Brescia, Italy)
Abstract:
We consider radial solutions to the Cauchy problem for a linear
wave equation with a small short-range electromagnetic potential
(depending on space and time) and zero initial data. We present
two dispersive estimates that provide, in particular, an optimal
decay rate in time $t^{-1}$ for the solution.
Also, we apply these estimates to obtain similar results for the
linear massless Dirac equation perturbed by a potential.
Submitted December 12, 2006. Published October 29, 2008.
Math Subject Classifications: 35A08, 35L05, 35L15, 58J37, 58J45.
Key Words: Wave equation; electromagnetic potential;
short-range; Dirac equation; dispersive estimate;
decay estimate.