Well-posedness and stability result for a swelling porous elastic system with neutral delay and porous damping

Abstract

This study takes into account a one-dimensional swelling porous elastic system with neutral delay and porous damping acting on the second equation. We verify the existence and uniqueness of the solution using the Faedo-Galerkin approach, and we prove that the porous damping dissipation is powerful enough to stabilize the system exponentially even in the presence of neutral delay using the multiplier method.