Noncompactness of integral operators modeling diffuse-gray radiation in polyhedral and transient settings
Please always quote using this URN:urn:nbn:de:0296-matheon-7408
- While it is well-known that the standard integral operator K of (stationary) diffuse-gray radiation, as it occurs in the radiosity equation, is compact if the domain of radiative interaction is sufficiently regular, we show noncompactness of the operator if the domain is polyhedral. We also show that a stationary operator is never compact when reinterpreted in a transient setting. Moreover, we provide new proofs, which do not use the compactness of K, for 1 being a simple eigenvalue of K for connected enclosures, and for I-(1-e)K being invertible, provided the emissivity e does not vanish identically.
Author: | Pierre-Etienne Druet, Peter Philip |
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URN: | urn:nbn:de:0296-matheon-7408 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/03/01 |
Release Date: | 2010/12/20 |
Tag: | |
Institute: | Technische Universität Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
MSC-Classification: | 45-XX INTEGRAL EQUATIONS / 45Axx Linear integral equations / 45A05 Linear integral equations |
45-XX INTEGRAL EQUATIONS / 45Cxx Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75] / 45C05 Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75] | |
45-XX INTEGRAL EQUATIONS / 45Exx Singular integral equations [See also 30E20, 30E25, 44A15, 44A35] / 45E99 None of the above, but in this section | |
45-XX INTEGRAL EQUATIONS / 45Pxx Integral operators [See also 47B38, 47G10] / 45P05 Integral operators [See also 47B38, 47G10] | |
Preprint Number: | 752 |