Stability analysis for a recovered fracturing fluid model in the wellbore of shale gas reservoir

Year 2023, Volume: 52 Issue: 6 - Special Issue: Nonlinear Evolution Problems with Applications , 1533 - 1549 , 03.11.2023

Jinxia Cen , Nicuşor Costea , Chao Min , Jen-chih Yao

https://doi.org/10.15672/hujms.1193699

https://izlik.org/JA69HP34KY

Abstract

This paper is concerned with the study of stability analysis to a complicated recovered frac- turing fluid model (RFFM, for short), which consists of a stationary incompressible Stokes equation involving multivalued and nonmonotone boundary conditions, and a reaction- diffusion equation with Neumann boundary conditions. Firstly, we introduce a family of perturbated problems corresponding to (RFFM) and deliver the variational formulation of perturbated problem which is a hemivariational inequality coupled with a variational equation. Then, we prove that the existence of weak solutions to perturbated problems and the solution sequence to perturbated problems are uniformly bounded. Finally, via employing Mosco convergent approach and the theory of nonsmooth, a stability result to (RFFM) is established.

Keywords

Recovered fracturing fluid model , stability analysis , hemivariational inequality , Clarke subgradient , Mosco convergence

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