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Well-posedness and general decay of a nonlinear damping porous-elastic system with infinite memory

In the present work, we consider a one-dimensional porous-elastic system with infinite memory and a nonlinear damping term. We establish the well-posedness of the system using semigroup theory and show the general decay for the case of nonequal speeds of wave propagation. Introducing some conditions on the kernel of the infinite memory term helps estimate the nonequal speed term even if this complementary control is not strong enough to stabilize the system exponentially. Our result is an extension of many other works in this area.