论文标题
在多层多孔介质中，半群理论应用于燃烧问题
Application of the semigroup theory to a combustion problem in a multi-layer porous medium
论文作者
论文摘要
这项研究证明，一维反应 - 扩散 - 转化系统的凯奇问题在$ \ mathtt {H}^2（\ Mathbb {r}）$中是本地和全球范围的。当每一层的燃料浓度是已知功能时，系统通过多层多孔介质建模了无气燃烧。燃烧具有关键的实用多孔媒体应用，例如在石油储层中的原位燃烧过程和其他几个领域。 较早的研究考虑了物理参数（例如孔隙率，导热率，热容量和初始燃料浓度）。在这里，我们考虑了一个更现实的模型，其中这些参数是空间变量而不是常数的函数。此外，在先前的研究中，我们没有考虑到本研究与当前研究不同的解决方案的连续性。该证明使用一种新颖的方法来燃烧多孔介质。我们遵循希尔伯特空间中运营商的抽象分数理论，以及众所周知的Kato理论，用于相关的初始价值问题。
This study proved that the Cauchy problem for a one-dimensional reaction-diffusion-convection system is locally and globally well-posed in $\mathtt{H}^2(\mathbb{R})$. The system modeled a gasless combustion front through a multi-layer porous medium when the fuel concentration in each layer was a known function. Combustion has critical practical porous media applications, such as in in-situ combustion processes in oil reservoirs and several other areas. Earlier studies considered physical parameters (e.g., porosity, thermal conductivity, heat capacity, and initial fuel concentration ) constant. Here, we consider a more realistic model where these parameters are functions of the spatial variable rather than constants. Furthermore, in previous studies, we did not consider the continuity of the solution regarding the initial data and parameters, unlike the current study. This proof uses a novel approach to combustion problems in porous media. We follow the abstract semigroups theory of operators in the Hilbert space and the well-known Kato's theory for a well-posed associated initial value problem.
