Bociu, LorenaMuha,  BorisWebster, Justin T.2022-10-072022-10-072023-06-20Bociu, Lorena, Boris Muha, and Justin T. Webster. “Mathematical Effects of Linear Visco-Elasticity in Quasi-Static Biot Models.” Journal of Mathematical Analysis and Applications 527, no. 2 (November 15, 2023): 127462. https://doi.org/10.1016/j.jmaa.2023.127462.https://doi.org/10.1016/j.jmaa.2023.127462http://hdl.handle.net/11603/26117We 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.20 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Text