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
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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