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Time Asymptotics for the Polyharmonic Wave Equation in Waveguides by P. H. Lesky is a Mathematics article available to read on EtoBox.
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## Abstract Let Ω denote an unbounded domain in R^__n__^ having the form Ω=R^__l__^×__D__ with bounded cross‐section __D__⊂R^__n__−__l__^, and let __m__∈N be fixed. This article considers solutions __u__ to the scalar wave equation ∂__u__(__t__,__x__) +(−Δ)^__m__^__u__(__t__,__x__) = __f__(__x__)e^−i__ωt__^ satisfying the homogeneous Dirichlet boundary condition. The asymptotic behaviour of __u__ as __t__→∞ is investigated. Depending on the choice of __f__ ,__ω__ and Ω, two cases occur: Either __u__ shows resonance, which means that ∣__u__(__t__,__x__)∣→∞ as __t__→∞ for almost every __x__ ∈ Ω, or __u__ satisfies the principle of limiting amplitude. Furthermore, the resolvent of the spatial operators and the validity of the principle of limiting absorption are studied. Copyright © 2003 John Wiley & Sons, Ltd.
Who reads Time Asymptotics for the Polyharmonic Wave Equation in Waveguides?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- P. H. Lesky
- Publisher
- John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 0170-4214)
- Published
- 2002
- Language
- EN
- Field
- Mathematics (Physical Sciences)