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Zero resonances in local perturbations of parallel-plane waveguidesHerrn Professor Rolf Leis zum 60. Geburtstag am 22·7·1991 gewidment (1990)

Werner, P.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 13 (1990), S. 111-136

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: In a joint paper with K. Morgenröther [9] we have studied the propagation of scalar waves in domains of the type Ω = Ωo-B̄ with Ωo:=∝2 × (0, 1), where B is a smooth bounded domain with B̄ ⊏ Ωo. In particular, we have shown that the solution of Neumann's initial and boundary value problem for the wave equation with time-independent right-hand side ƒ increases with a logarithmic rate as t → ∞ if the integral over ƒ does not vanish. The main purpose of the present paper is to extend this result to arbitrary smooth local perturbations of Ωo.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/mma.1670130203

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