ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
In part 1Math. meth. in the Appl. Sci, 10, 125-144 (1988). we studied the principle of limiting absorption for local perturbations Ω of the n-dimensional domain Ω0 = ∝n-1 × (0, π). In this second part we extend our investigations to the time-dependent theory and show that absence of admissible standing waves implies the validity of the principle of limiting amplitude for every frequency ω≥0 if n ≠ 3 and for ω ≠ 2, 3,… if n = 3, respectively. In particular, the principle of limiting amplitude holds for every ω≥0 in the case n ≠ 3 and for every ω ≠ 2, 3,… in the case n = 3 if Ω≠Ω0 and ν·x′ ≤0 on ∂Ω, where x′ = (x1,…, xn-1, 0) and ν is the normal unit vector on ∂Ω pointing into the complement of Ω This result stands in remarkable contrast to the fact that both principles are violated in the case of the unperturbed domain Ω0 at the frequencies ω = 1, 2,… if n≤3. The question of the asymptotic behaviour of the solution as t→∞ for n = 3 and ω = 2, 3,… will be discussed in two subsequent papers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670110101
