RT Journal Article
T1 Decay for strain gradient porous elastic waves
A1 González Baldonedo, Jacobo
A1 Fernández García, José Ramón
A1 Magaña, Antonio
A1 Quintanilla, Ramón
K1 12 Matemáticas
K1 1206 Análisis Numérico
K1 1202 Análisis y Análisis Funcional
AB 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.
PB Zeitschrift für angewandte Mathematik und Physik
SN 00442275
YR 2023
FD 2023-01-05
LK http://hdl.handle.net/11093/4598
UL http://hdl.handle.net/11093/4598
LA eng
NO Zeitschrift für angewandte Mathematik und Physik, 74(35): 1-25 (2023)
NO Agencia Estatal de Investigación | Ref. PGC2018‐096696‐B‐I00
DS Investigo
RD 15-mar-2025