Theoretical study and numerical test for a delayed thermoelastic porous system with microtemperatures

Abstract This research paper aims to investigate a one‐dimensional thermoelastic porous system with microtemperatures effects in the presence of discrete time delay in internal feedback without frictional damping to control the delay term. First, we establish the well‐posedness of the system using semigroup theory. Then, based on the energy method we show an exponential stability result of the solution, under a smallness condition on the delay, irrespective of the wave speeds of the system or any other condition on the coefficients. Finally, we give numerical experiments to validate our theoretical result by carrying out an Euler scheme for time discretization and the classical finite difference method for the spatial discretization. The existing findings have been enhanced and present novel advancements compared to the established results in the literature.