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Title: | Dispersive Estimate for the Wave Equation with Short-Range Potential | Authors: | Visciglia, Nicola | Keywords: | dispersive estimates; resolvent estimates; Wave Equation with potential | Issue Date: | 2003 | Publisher: | Università degli Studi di Trieste. Dipartimento di Matematica e Informatica | Source: | Nicola Visciglia, "Dispersive Estimate for the Wave Equation with Short-Range Potential", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 35 (2003), pp. 117–145. | Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics 35 (2003) |
Abstract: | In this paper we consider a potential type perturbation of the three dimensional wave equation: $\Box u + V(x)u = 0 u(x, 0) = 0, \partial_t u(x, 0) = f$, where the potential $V \geq 0$ satisfies the following decay assumption: $|V (x)| \leq \frac{C}{1+|x|^{2+\epsilon_0}}$, for some C, $\epsilon_0 > 0$. We establish some dispersive estimates for the associated propagator. |
Type: | Article | URI: | http://hdl.handle.net/10077/4195 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.35 (2003) |
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