Scattering properties of wave equations with time-dependent potentials
β Scribed by G.Perla Menzala
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 716 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0898-1221
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π SIMILAR VOLUMES
## Abstract We consider the following semilinear wave equation: equation image for (__t__,__x__) β β~__t__~ Γ β. We prove that if the potential __V__(__t__,__x__) is a measurable function that satisfies the following decay assumption: β£__V__(__t__,__x__)β£β©½__C__(1+__t__)(1+β£__x__β£) for a.e. (__t_
## Abstract We study the initialβboundary value problem for β~__t__~^2^__u__(__t__,__x__)+__A__(__t__)__u__(__t__,__x__)+__B__(__t__)β~__t__~__u__(__t__,__x__)=__f__(__t__,__x__) on [0,__T__]ΓΞ©(Ξ©ββ^__n__^) with a homogeneous Dirichlet boundary condition; here __A__(__t__) denotes a family of unifor
We study the asymptotic behavior of solutions of dissipative wave equations with space-time-dependent potential. When the potential is only time-dependent, Fourier analysis is a useful tool to derive sharp decay estimates for solutions. When the potential is only space-dependent, a powerful techniqu