We consider a boundary value problem (BVP) modelling one-dimensional heat-conduction with radiation, which is derived from the Stefan-Boltzmann law. The problem strongly depends on the parameters, making difficult to estimate the solution. We use an analytical approach to determine upper and lower bounds to the exact solution of the BVP, which allows estimating the latter. Finally, we support our theoretical arguments with numerical data, by implementing them into the MAPLE computer program.

翻译：我们考虑一个基于斯特藩-玻尔兹曼定律导出的、模拟一维热传导辐射过程的边值问题（BVP）。该问题强烈依赖于参数，导致解的估计十分困难。我们采用解析方法确定该边值问题精确解的上下界，从而实现对解的估计。最后，我们将这些理论论证通过MAPLE计算机程序实现，并利用数值数据加以验证。