Theoretical Decay Results of a Swelling Soils System with Frictional Damping Versus Viscoelastic Damping

We consider a swelling porous-elastic system with frictional damping and viscoelastic damping acting simultaneously and complementarily in the domain and study the effect of such competition between the two types of damping on the asymptotic behavior of the energy function. Under nonrestrictive on the growth assumption on the frictional damping and under more general assumption on the relaxation function, we establish, for the first time as per our knowledge, explicit and optimal energy decay rates for this system. Our decay results were obtained by using the multiplier method and some properties of the convex functions. These results generalize and improve some earlier related results in the literature.