Beschreibung:
<jats:title>Abstract</jats:title><jats:p>In the current study, we analyze the asymptotic behavior of the solutions of one‐dimensional initial boundary value problem associated with the isothermal linear theory of swelling porous elastic media. Our main results are the well‐posedness of the system as well as the exponential stabilization of solution and the discretization of the equations using a particular numerical scheme, which allowed us to prove the monotonicity of the discrete energy. In addition, we provide the numerical simulations of the solution and the total energy that explain the results obtained. Our results are achieved by using the semigroup theory and for the results in finite dimensional we used finite differences.</jats:p>