We investigate nonlinear stability in a model for thermal convection in a saturated porous material using Brinkman theory, taking into account viscous dissipation effects. There are (at least) two models for viscous dissipation available, and we include a derivation of one of these by assuming that the flow in the porous medium may be described by a theory for a mixture of an elastic solid and a linearly viscous fluid. A fully nonlinear stability result is provided when either of the viscous dissipation functions is taken into account, and it is shown that from the nonlinear energy stability viewpoint both models are, in a sense, equivalent.

中文翻译：

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具有粘性耗散的 Brinkman 多孔材料中热对流的非线性稳定性

我们使用 Brinkman 理论研究饱和多孔材料热对流模型中的非线性稳定性，同时考虑了粘性耗散效应。有（至少）两种可用的粘性耗散模型，我们通过假设多孔介质中的流动可以用弹性固体和线性粘性流体的混合物的理论来描述，我们包括其中一个的推导。当考虑任何一个粘性耗散函数时，都提供了完全非线性的稳定性结果，并且表明从非线性能量稳定性的角度来看，两种模型在某种意义上是等效的。