Abstract We study global dynamics of phase transition evaporation interfaces in horizontally extended domains of porous layers where a water located over a vapor. The derivation of the model equation describing the secondary structures, which bifurcate from the ground state in a small neighborhood of the instability threshold in the case of a quasi-stationary approach to the description of the diffusion process, is presented. The resulting equation is reduced to the equation in the form of Kolmogorov-Petrovsky-Piskounov. The obtained approximate equation predicts the existence of stationary solutions in the full problem. To verify the obtained results, the numerical solution of the problem of the motion of the phase transition interface is performed using the original program code developed by the authors. The results of numerical simulation are used to verify the possibility of using stationary solutions obtained in the weakly nonlinear approximation to determine the scenario for the development of the initial localized finite amplitude perturbation. It is shown that the obtained approximate stationary solutions accurately predict the behavior of the perturbation in the vicinity of the turning point of the bifurcation diagram. A modification of the formulas describing an approximate stationary soliton-like solution is proposed in the case when the perturbation amplitude is comparable with the height of a low-permeable layer of a porous medium in which the phase transition interface is located. By numerical simulation it is shown that this modified approximate solution is in good agreement with the results of numerical calculation for the full problem.

中文翻译：

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一个多孔介质中水分蒸发问题的相变界面有限微扰的稳定性

摘要 我们研究了多孔层水平扩展域中相变蒸发界面的全局动力学，其中水位于蒸汽上方。介绍了描述二级结构的模型方程的推导，在描述扩散过程的准平稳方法的情况下，二级结构从不稳定阈值的小邻域中的基态分叉。得到的方程简化为 Kolmogorov-Petrovsky-Piskounov 形式的方程。得到的近似方程预测了完整问题中平稳解的存在。为了验证所得结果，使用作者开发的原始程序代码对相变界面的运动问题进行了数值求解。数值模拟的结果被用来验证使用在弱非线性近似中获得的平稳解来确定初始局部有限振幅扰动的发展情景的可能性。结果表明，得到的近似平稳解准确地预测了分岔图转折点附近的扰动行为。在扰动幅度与相变界面所在的多孔介质的低渗透层的高度相当的情况下，提出了对描述近似稳态孤子解的公式的修改。