Analyticity to transmission problem with delay in porous-elasticity

In this paper, we consider a one-dimensional transmission problem in a bounded domain with a delay in porous-elasticity. Using a semigroup theorem, under suitable assumption on the weight of the delay term, we establish the well-posedness of the system. Furthermore, using the method developed by Z. Liu and S. Zheng we show that the semigroup associated with the dissipative system is analytic and consequently exponentially stable.