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Stefan–Boltzmann Radiation on Non‐convex Surfaces
Author(s) -
Tiihonen T.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970110)20:1<47::aid-mma847>3.0.co;2-b
Subject(s) - mathematics , monotone polygon , regular polygon , boundary value problem , monotonic function , boundary (topology) , infinity , mathematical analysis , geometry
We consider the stationary heat equation for a non‐convex body with Stefan–Boltzmann radiation condition on the surface. The main virtue of the resulting problem is non‐locality of the boundary condition. Moreover, the problem is non‐linear and in the general case also non‐coercive and non‐monotone. We show that the boundary value problem has a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. In the two dimensional case or when a part of the radiation can escape the system we obtain coercivity and stronger existence result. © 1997 by B.G. Teubner Stuttgart‐John Wiley & Sons, Ltd.