On a nonlinear system of Biot–Forchheimer type
Youcef Atik, Hacina Kabir, Guy Vallet · Complex Variables and Elliptic Equations · 2019
We analyse a nonlinear parabolic/elliptic system describing the high-velocity flow of a fluid in a poro-elastic medium. Based on a time discretization of the parabolic equation and monotone arguments, we prove a result of well-posedness of the problem in the sense of Hadamard. In addition, the strong convergence of the sequence of approximations is proved.