# Solvability of the mixed formulation for generalized Forchheimer flows of isentropic gases

## TL;DR

This paper investigates the solvability of the mixed formulation for generalized Forchheimer flows of isentropic gases, establishing existence and uniqueness results for both stationary and time-dependent problems using semi-discretization techniques.

## Contribution

It provides the first rigorous proof of existence and uniqueness for the mixed formulation of these nonlinear flows, including both stationary and time-dependent cases.

## Key findings

- Existence and uniqueness of solutions for the stationary problem.
- Existence of solutions for the time-dependent problem via semi-discretization.
- Rigorous mathematical framework for generalized Forchheimer flows.

## Abstract

This paper is focused on the generalized Forchheimer flows of isentropic gas, described by a system of two nonlinear degenerating differential equations of first order. We prove the existence and uniqueness of the Dirichlet problem for stationary problem. The technique of semi-discretization in time is used to prove the existence for the time-dependent problem.