Electron. J. Diff. Eqns., Vol. 2008(2008), No. 150, pp. 1-12.

Dispersive estimates for a linear wave equation with electromagnetic potential

Davide Catania

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.

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Davide Catania
Dipartimento di Matematica, Facoltà di Ingegneria
Università di Brescia, Via Valotti 9, 25133 Brescia, Italy
email: catania@ing.unibs.it

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