We study a nonlinear problem of gas filtration in a porous and weakly conducting medium that is used to model the overheating process in reactors. We obtain explicit estimates for the critical values of the similarity parameter of the problem which determine a condition for the existence of a steady-state cooling regime for a system open to atmosphere and a condition for global overheating. The bifurcation point is determined for the original system of equations. There is a thin layer in which the heat energy is concentrated at high temperatures. It is shown that, at the bifurcation point, the convection process is replaced by the process of molecular thermal conductivity described by a nonlinear integro-differential equation.

中文翻译：

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Maslov事故反应堆中的静态冷却，过热和能量局部化模型

我们研究了在多孔弱导电介质中气体过滤的非线性问题，该问题用于模拟反应堆中的过热过程。我们获得问题相似性参数临界值的显式估计值，这些估计值确定了对大气开放的系统存在稳态冷却状态的条件以及对全局过热的条件。对于原始方程组，确定分叉点。有一个薄层，其中热能在高温下集中。结果表明，在分叉点处，对流过程被非线性积分微分方程描述的分子导热过程所代替。