Stefan-Boltzmann Radiation on Non-convex Surfaces

Abstract

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.