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.