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<p>In this work, we consider the porous elastic system with weak damping acting in the displacement equation. We combine semigroup theory with the energy method. For the existence and uniqueness of solution, we apply the Gearhart-Herbst-Prüss-Huang Theorem. For the asymptotical behavior, we establish the exponential stability, lack of exponential stability, and polynomial decay with optimal rate, depending on a relationship between the system’s coefficients, that is, we consider the cases of equal and nonequal speeds of wave propagation. We also performed a numerical test to illustrate our theoretical result.</p>

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Porous Elastic System with Weak Damping Acting on the Material Displacement Equation

  • 期刊论文

  • 发表日期：

    2025年10月2日

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  • Luiz Gutemberg R. Miranda,
  • Carlos A. Raposo,
  • Lindomar M. Ribeiro,
  • Juarez S. Azevedo

摘要

In this work, we consider the porous elastic system with weak damping acting in the displacement equation. We combine semigroup theory with the energy method. For the existence and uniqueness of solution, we apply the Gearhart-Herbst-Prüss-Huang Theorem. For the asymptotical behavior, we establish the exponential stability, lack of exponential stability, and polynomial decay with optimal rate, depending on a relationship between the system’s coefficients, that is, we consider the cases of equal and nonequal speeds of wave propagation. We also performed a numerical test to illustrate our theoretical result.