EXPONENTIAL DECAY IN ONE-DIMENSIONAL POROUS DISSIPATION ELASTICITY

Of concern in this work is a linear one-dimensional porous-elastic system with dissipation only on the porous equation. It is well-known in the literature that the system with such dissipation is not exponentially stable unless another damping mechanisms are added to the system. Contrarily, in this article, we prove that the dissipation is strong enough to exponentially stabilize the system, provided the wave speeds are equal. The result is new and opens more research areas into porous-elastic system.