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：我们考虑一个由斯特藩-玻尔兹曼定律导出的、模拟一维热传导与辐射的边值问题。该问题强烈依赖于参数，使得解的估计变得困难。我们采用解析方法确定该边值问题精确解的上下界，从而实现对解的有效估计。最后，通过将上述方法在MAPLE计算机程序中实现，我们利用数值数据支撑了理论论证。