2023 journal article
Mathematical effects of linear visco-elasticity in quasi-static Biot models ✩
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 527(2).
author keywords: Poroelasticity; Implicit evolution equations; Strong damping; Viscoelasticity
TL;DR:
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.
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open access via arxiv.org (repository)
Source: Web Of Science
Added: August 7, 2023
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.