2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal,
Electron. J. Diff. Eqns., Conference 22 (2015), pp. 1-18.

Mathematical analysis of a viscoelastic-gravitational layered earth model for magmatic intrusion in the dynamic case

Alicia Arjona, Jesus Ildefonso Diaz

Volcanic areas present a lower effective viscosity than usually in the Earth's crust. It makes necessary to consider inelastic properties in deformation modelling. As a continuation of work done previously by some of the authors, this work is concerned with the proof that the perturbed equations representing the viscoelastic-gravitational displacements resulting from body forces embedded in a layered Earth model leads to a well-posed problem even for any kind of domains, with the natural boundary and transmission conditions. A homogeneous or stratified viscoelastic half-space has often been used as a simple earth model to calculate the displacements and gravity changes. Here we give a constructive proof of the existence of weak solutions and we show the uniqueness and the continuous dependence with respect to the initial data of weak solutions of the dynamic coupled viscoelastic-gravitational field equations.

Published November 20, 2015.
Math Subject Classifications: 35K10, 35L10, 35Q86, 35Q74, 46E35, 86A60.
Key Words: Gravity changes; viscoelastic-gravitational earth model; weak solution; iterative algorithm; continuous dependence; uniqueness of solutions.

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Alicia Arjona
European Center for Geodynamics and Seismology
Rue Josy Welter, 19, L-7256 Walferdange
Gran-Duchy of Luxembourg
email: alicia.arj@gmail.com
Jesús Ildefonso Díiaz
Departamento de Matemática Aplicada
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
Plaza de las Ciencias, 3, 28040 Madrid, Spain
email: jidiaz@ucm.es

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