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Stabilization of swelling porous elastic soils with fluid saturation by one internal damping

This article considers the stabilization of a system of one-dimensional swelling porous elastic soils with fluid saturation. This system is strongly coupled by vibrations of both fluid and solid elastic materials. Using Riesz basis approach, it is shown that the system can be exponentially stabilized by one internal damping with variable feedback gain imposed in the fluid equation. The result improved greatly at the first time the previous results in literature where two dampings are needed to get the same result.