Stabilization of a hyperbolic/ellipticsystem modelling the viscoelastic-gravitationaldeformation in a multilayeredEarth

Alicia  Arjona; Jesús Ildefonso Díaz

doi:10.3934/proc.2015.0066

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2015, Volume 2015: 66-74. Doi: 10.3934/proc.2015.0066 open access

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Stabilization of a hyperbolic/elliptic system modelling the viscoelastic-gravitational deformation in a multilayered Earth

Alicia Arjona^1, and
Jesús Ildefonso Díaz^2,

1.
European Center for Geodynamics and Seismology, Rue Josy Welter, 19. L-7256, Walferdange, Grand-Duchy of Luxembourg
2.
Instituto de Matemática Interdisciplinar and Dpto. Mat. Aplicada. (UCM), Facultad de Matemáticas, Plaza de las Ciencias, 3. 28040, Madrid

Received: August 31, 2014

Revised: November 30, 2014

Published: October 2015

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Abstract

In the last 30 years several mathematical studies have been devoted to the viscoelastic-gravitational coupling in stationary and transient regimes either for static case or for hyperbolic case. However, to the best of our knowledge there is a lack of mathematical study of the stabilization as $t$ goes to infinity of a viscoelastic-gravitational models crustal deformations of multilayered Earth. Here we prove that, under some additional conditions on the data, the difference of the viscoelastic and elastic solutions converges to zero, as $t$ goes to infinity, in a suitable functional space. The proof of that uses a reformulation of the hyperbolic/elliptic system in terms of a nonlocal hyperbolic system.

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Mathematics Subject Classification: 34H15, 37B25, 35Q74, 35Q84.

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References

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