Numerical stabilization for a mixture system with kind damping

TL;DR

This paper analyzes the numerical stabilization and decay rates of a complex mixture system modeling rigid solids with porosity, providing conditions for stabilization and insights into system dynamics through simulations.

Contribution

It offers a novel numerical analysis of stabilization conditions and decay rates for a mixture system with complex interactions, which was not previously rigorously quantified.

Findings

Established conditions for strong stabilization and polynomial decay.

Numerical simulations demonstrate the effectiveness of stabilization mechanisms.

Analyzed the influence of system parameters on decay rates.

Abstract

In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with porosity. This mathematical model accounts for the complex interactions between the rigid components and their porous structure, providing valuable information on the mechanical behavior of such systems. Our primary objective is to establish conditions under which stabilization is ensured and to rigorously quantify the rate of decay of the solutions. Using numerical simulations, we assess the effectiveness of different stabilization mechanisms and analyze the influence of key system parameters on the overall dynamics.