Details

Autor(en) / Beteiligte

• Baldonedo, Jacobo
• Fernández, José R.
• Magaña, Antonio
• Quintanilla, Ramón

Titel

Decay for strain gradient porous elastic waves

Ist Teil von

• Zeitschrift für angewandte Mathematik und Physik, 2023-02, Vol.74 (1), Article 35

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the one-dimensional problem for the linear strain gradient porous elasticity. Our aim is to analyze the behavior of the solutions with respect to the time variable when a dissipative structural mechanism is introduced in the system. We consider five different scenarios: hyperviscosity and viscosity for the displacement component and hyperviscoporosity, viscoporosity and weak viscoporosity for the porous component. We only apply one of these mechanisms at a time. We obtain the exponential decay of the solutions in the case of viscosity and a similar result for the viscoporosity. Nevertheless, in the hyperviscosity case (respectively hyperviscoporosity) the decay is slow and it can be controlled at least by t - 1 / 2 . Slow decay is also expected for the weak viscoporosity in the generic case, although a particular combination of the constitutive parameters leads to the exponential decay. We want to emphasize the fact that the hyperviscosity (respectively hyperviscoporosity) is a stronger dissipative mechanism than the viscosity (respectively viscoporosity); however, in this situation, the second mechanism seems to be more “efficient” than the first one in order to pull along the solutions rapidly to zero. This is a striking fact that we have not seen previously at any other linear coupling system. Finally, we also present some numerical simulations by using the finite element method and the Newmark- β scheme to show the behavior of the energy decay of the solutions to the above problems, including a comparison between the hyperviscosity and the viscosity cases.