Biot’s poro-elasticity system with dynamic permeability convolution: Well-posedness for evolutionary form

We consider Biot's equations of poroelasticity where the development of viscous boundary layers in the pores is allowed for by using a dynamic permeability convolution operator in the time domain. This system with memory effects is also referred to as the dynamic Biot–Allard model. We use a series representation of the dynamic permeability in the frequency domain to rewrite the equations in the time domain in a coupled system without convolution integrals, which is also suitable for designing efficient numerical approximation schemes. The main result here is the well-posedness of the system, rewritten in evolutionary form, which is proved by an abstract theory for evolutionary problems.