Mathematical Effects of Linear Visco-elasticity in Quasi-static Biot Models

2022/08/24 by Bociu, Lorena, Muha, Boris, Webster, Justin T. · 2 citations
#35A01 #35B65 #35M13 #35Q86 #35Q92 #74F10 #76S05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.11653

Abstract

We investigate and clarify the mathematical properties of linear poro-elastic systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time-regularizing and dissipative effects of visco-elasticity in the context of the quasi-static Biot equations. The full, coupled pressure-displacement presentation of the system is utilized, as well as the framework of implicit, degenerate evolution equations, to demonstrate such effects and characterize linear poro-visco-elastic systems. We consider a simple presentation of the dynamics (with convenient boundary conditions, etc.) for clarity in exposition across several relevant parameter ranges. Clear well-posedness results are provided, with associated a priori estimates on the solutions. In addition, precise statements of admissible initial conditions in each scenario are given.

Cited by

• Local Well-Posedness of the Cahn-Hilliard-Biot System
• Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions

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