On the control of viscoelastic damped swelling porous elastic soils with internal delay feedbacks

Abstract

We consider a swelling porous-elastic system with viscoelastic damping and delay feedbacks acting on the fluid equation. Using the multiplier method and under the well-known assumption on the weight of delay term, we unexpectedly establish a general decay result without imposing the usual condition of equal wave speeds of the system, unlike the case of Timoshenko and porous systems where damping on only one of the equations requires equal wave speeds propagation. Our coupling and the result give new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils.