On the behavior of some porous thermoelastic

In this thesis, we investigate the longtime behavior of certain porous thermoelastic systems
characterized by type-III thermoelasticity. Specifically, we study three problems, two
of which involve delay terms.
The first problem addresses a porous thermoelastic system in which the heat conduction
is governed by the type III law of Green and Naghedi, and incorporating a constant delay
term. We examined both equal and non-equal wave speed scenarios. In both cases, we established
a well-posedness result using a semigroup approach and the Hille-Yosida theorem.
Additionally, for the case of equal speeds, we demonstrated that an exponential rate of decay
occurs provides an inequality between the weights of the delay and thermal dissipation.
Conversely, in the case of unequal speeds, we derived a polynomial rate of decay. In both
scenarios, we employed multiplier and energy methods.
In the second problem, we replaced the constant delay from the first problem with a
distributed delay term. The results obtained are similar to those of the first problem.
The third problem addressed a porous thermoelastic system characterized by Type-
III thermoelasticity and a nonlinear damping term acting in the porous equation. We
established a well-posedness result and demonstrated an explicit general decay result in
the case of equal wave speeds. This was accomplished by employing properties of convex
functions and the multiplier method.