Filtration in Composite Incompressible Media
Anvarbek Mukatovich Meirmanov · Atlantis studies in differential equations · 2013
This chapter is devoted to filtration from reservoirs into porous media under gravity, and filtration in poroelastic media with variable pore space structure. The second problem consists of two different settings and based on the problem for two different poroelastic media with a common boundary. In the first setting we consider an arbitrary partition $$\varPi ^{(\delta )}=\{K^{(\delta )}_{1},...,K^{(\delta )}_{N_{\delta }}\}$$ of the domain $$\varOmega $$ , where the structure of $$K^{(\delta )}_{j}$$ is defined by the characteristic function $$\chi ^{(\varepsilon ,\delta )}$$ , and pass to the limit as $$\varepsilon \rightarrow 0$$ . After that we pass to the limit as $$\delta \rightarrow 0$$ . In the second setting we consider the same partition, but firstly pass to the limit as $$\delta \rightarrow 0$$ and after that pass to the limit as $$\varepsilon \rightarrow 0$$ . In both cases we obtain the same result. As basic models at the microscopic level we consider mathematical models $$\mathbb {M}_{24}$$ and $$\mathbb {M}_{15}$$ . Here we will keep the same notation as in previous chapters.