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Andres Franco Grisales: Asymptotics of silent wave equations

Time: Thu 2023-04-27 10.15 - 11.15

Location: 3418, Lindstedtsvägen 25

Language: English

Participating: Andres Franco Grisales, KTH

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We study the asymptotics of a particular class of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by the asymptotic data contained in the estimates. As an application, we then study solutions to source free Maxwell's equations in Kasner spacetime near the initial singularity. Our results then allow us to obtain an asymptotic expansion for the electromagnetic potential, and to show that the energy density of generic solutions blows up along generic timelike geodesics when approaching the singularity.