Propagation of boundary-induced discontinuity in stationary radiative transfer
| Autor: | I.-Kun Chen, Daisuke Kawagoe |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Boundary (topology)
FOS: Physical sciences Discontinuity 01 natural sciences Domain (mathematical analysis) Mathematics - Analysis of PDEs Characteristic lines Radiative transfer FOS: Mathematics Boundary value problem 0101 mathematics Mathematical Physics Physics 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics 70B05 Mathematical Physics (math-ph) 010101 applied mathematics Discontinuity (linguistics) Stationary transport equation Piecewise Slab Convection–diffusion equation Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1707.09182 |
| Popis: | We consider the boundary value problem of the stationary transport equation in the slab domain of general dimensions. In this paper, we discuss the relation between discontinuity of the incoming boundary data and that of the solution to the stationary transport equation. We introduce two conditions posed on the boundary data so that discontinuity of the boundary data propagates along positive characteristic lines as that of the solution to the stationary transport equation. Our analysis does not depend on the celebrated velocity averaging lemma, which is different from previous works. We also introduce an example in two dimensional case which shows that piecewise continuity of the boundary data is not a sufficient condition for the main result. Comment: 15 pages, no figures |
| Databáze: | OpenAIRE |
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