General decay for a porous-thermoelastic system with memory: The case of nonequal speeds

Asymptotical stability for memory‐type porous thermoelastic system of type III with constant time delay

“…Soufyane studied the porous equation together with a microtemperature effect and a viscoelastic damping effect and showed the exponential (polynomial) decay when the relaxation function decays exponentially (polynomially). And then Messaoudi and Fareh studied the following system, and established the general decay result when (equal propagation speeds) and (nonequal propagation speeds), respectively. And the exponential and the polynomial results in are merely special cases.…”

Exponential decay of solution to the viscoelastic porous‐thermoelastic system of type III with boundary time‐varying delay

“…Messaoudi and Fareh studied the following porous‐thermoelastic system with a viscoelastic damping, and proved a general decay of when and , respectively.…”

“…Messaoudi and Fareh [8,9] studied the following porous-thermoelastic system with a viscoelastic damping, 4) and proved a general decay of (1.4) when k 1 D˛ 2 and k 1 ¤˛ 2 , respectively. Messaoudi and Apalara [10] considered (1.1) without boundary time delay and proved exponential stability when k 1 D˛ 2 , and polynomial delay when k 1 ¤˛ 2 .…”

On the decay rates for a one-dimensional porous elasticity system with past history

“…Under the assumption g (t) ≤ −ξ(t)g(t), they established a general decay for the energy in the case of equal wave speeds in [20], and in the case of nonequal speeds in [21]. The author of the present work, Feng [10], studied the general model (8) with past history, i.e., the memory term in the second equation is replaced by…”

“…Under the assumption g (t) ≤ −κg p (t), the author proved the system is exponential decay if p = 1 and polynomial decay if 1 < p < 3/2. Messaoudi and Fareh [20,21] considered a more general system than the one in [34]:…”