A nonlocal problem arising from heat radiation on non-convex surfaces. (English) Zbl 0889.45013

Tiihonen, T.

Eur. J. Appl. Math. 8, No. 4, 403-416 (1997).

The paper is an improvement of another study, recently published by the author in [Math. Methods. Appl. Sci. 20, No. 1, 47-57 (1997; Zbl 0872.35044)] whose knowledge is necessary for a good understanding of the present one. He studies the stationary and nonstationary heat equations for convex and nonconvex bodies, connex or nonconnex, with Stefan-Boltzmann radiation conditions on the surface. The temperature propagates through conduction, convection and radiation. The consideration of nonconvex bodies complicates very much the mathematical problem with the nonlocality of the boundary condition and with its noncoercivity.
Under these conditions, the author proves the existence of a weak solution by the introduction of upper and lower solutions which assure, underfsome hypotheses, the existence of subsolutions and supersolutions. It ends with a short chapter, where the author presents some other problems resulting from the study made in the paper.

Reviewer: V.Ionescu (Bucureşti)

MSC:

45K05	Integro-partial differential equations
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

non-convex surfaces; nonstationary heat equations; Stefan-Boltzmann radiation; weak solution; upper and lower solutions; subsolutions; supersolutions

Citations:

Zbl 0872.35044