Weak solutions to a stationary heat equation with nonlocal radiation boundary condition and right‐hand side in <i>L</i>^<i>p</i> (<i>p</i>⩾1)

Abstract

Abstract Accurate modelling of heat transfer in high‐temperature situations requires accounting for the effect of heat radiation. In complex industrial applications involving dissipative heating, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L 1 . In this paper, we focus on a stationary heat equation with nonlocal boundary conditions and L p right‐hand side, with p ⩾1 being arbitrary. Thanks to new coercivity results, we are able to produce energy estimates that involve only the L p norm of the heat sources and to prove the existence of weak solutions. Copyright © 2008 John Wiley &amp; Sons, Ltd.