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DC Field | Value | Language |
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dc.contributor.author | Chandler-Wilde, SN | - |
dc.contributor.author | Peplow, AT | - |
dc.coverage.spatial | 24 | en |
dc.date.accessioned | 2008-05-23T14:12:08Z | - |
dc.date.available | 2008-05-23T14:12:08Z | - |
dc.date.issued | 1994 | - |
dc.identifier.citation | Maths Technical Papers (Brunel University). April 1994, pp 1-20 | en |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/2282 | - |
dc.description.abstract | We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground. | en |
dc.format.extent | 360437 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | Brunel University | en |
dc.relation.ispartof | Brunel University Mathematics Technical Papers collection | - |
dc.relation.ispartofseries | TR/04/94 | - |
dc.title | Asymptotic behaviour at infinity of solutions of second kind integral equations on unbounded regions of Rn | en |
dc.type | Research Paper | en |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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TR_04_94.pdf | 351.99 kB | Adobe PDF | View/Open |
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