Details

Autor(en) / Beteiligte

• Bociu, Lorena
• Muha, Boris
• Webster, Justin T.

Titel

Mathematical effects of linear visco-elasticity in quasi-static Biot models

Ist Teil von

• Journal of mathematical analysis and applications, 2023-11, Vol.527 (2), p.127462, Article 127462

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.