We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing reacting solutes medium. investigate well-posedness of nonlinear set equations fixed-point theory, Fredholm's alternative, priori estimates, compactness arguments. also propose finite element method rigorously demonstrat...

In this paper we investigate the limit behavior of the solution to quasi-static Biot’s equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by Marciniak-Czochra and Mikelić in [16]. We choose Terzaghi’s time corresponding to the shell thickness and obtain the strong convergence of the three-dimensiona...

Poroelastic materials are often used as sound and vibration reduction measures in many engineering applications. Their dynamic behaviour is accurately described by the theory of Biot. The Finite Element Method is most commonly used to simulate such materials, however, is only applicable for low-frequency applications due to the associated computational cost. This extended abstract describes the...