On a nonlinear system of Biot–Forchheimer type. Issue 12 (1st December 2020)

• Record Type: Journal Article
• Authors: Atik, Y.; Kabir, H.; Vallet, G.
• Is Part Of: Complex variables and elliptic equations. Volume 65:Issue 12(2020)
• Page Start: 2112
• Page End: 2134
• Publication Date: 2020-12-01
• Subjects: V. Volpert; Nonlinear system -- strictly monotone -- Biot -- Forchheimer; 74F10 -- 35M32 -- 76S05; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2019.1695786
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : 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.