Advanced Search
Article Contents
Article Contents

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

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: 34H15, 37B25, 35Q74, 35Q84.


    \begin{equation} \\ \end{equation}
  • [1]

    A. Arjona, J.I. Díaz, J. Fernández and J.B. Rundle, On the Mathematical Analysis of an Elastic-gravitational Layered Earth Model for Magmatic Intrusion: The Stationary Case, Pure Appl. Geophys., 165 (2008), 1465-1490.


    A. Arjona and J.I. Díaz, On the mathematical analysis of a viscoealstic-gravitational layered earth model for magmatic intrusion: The dynamic Case, Submitted.


    T. Cazenave and A. Haraux, Introduction aux Problèmes d'évolution Semi-Linéaires. Ellipses , Paris, 1990.


    J.I. Díaz and F. de Thelin, On a nonlinear parabolic problems arising in some models related to turbulence flows, SIAM Journal of Mathematical Analysis, 25 (1994), 1085-1111.


    J. Fernández, J.M. Carrasco, J.B. Rundle and V. Araña, Geodetic methods for detecting volcanic unrest: a theoretical approach, Bulletin of Volcanology, 60 (1999), 534-544.


    J. Fernández, M. Charco, K.F. Tiampo, G. Jentzsch and J.B. Rundle, Joint interpretation of displacement and gravity data in volcanic areas. A test example: Long Valley Caldera, California, J.Volcanology and Geothermal Research, 28 (2001), 1063-1066.


    J. Fernández and J.B. Rundle, Postseismic visoelastic-gravitational half space computations: Problems and solutions, Geophysical Research Letters, 31 (2004).


    A. Folch, J. Fernández, J.B. Rundle and J. Martí, Ground deformation in a viscoelastic medium composed of a layer overlying a half space: A comparison between point and extended sources, Geophys.J.Int., 140 (2000), 37-50.


    A.E.H. Love, Some problems in Geodynamics, Cambridge University Press, New York, 1911.


    J.B. Rundle, Static elastic-gravitational deformation of a layared half space by point couple sources, J. Geophys.Res., 85 (1980), 5355-5363.


    J.B. Rundle, Numerical Evaluation of static elastic-gravitational deformation of a layared half space by point couple sources, Rep., Sandia National Lab., Albuquerque, NM, SAND80-2048., (1980), 2048.


    J.B. Rundle, Deformation, gravity and potential changes due to volcanic loading of the crust, J. Geophys.R, 87 (1982), 10.729-10.744.


    J.B. Rundle, Viscoeslastic-Gravitational Deformation by a Rectangular Thrust Fault in a Layered Earth, J. Geophys.Res., 87 (1982b), 7787-7796.

  • 加载中
Open Access Under a Creative Commons license

Article Metrics

HTML views() PDF downloads(73) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint