2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal,
Electron. J. Diff. Eqns., Conference 22 (2015), pp. 118.
Mathematical analysis of a viscoelasticgravitational
layered earth model for magmatic intrusion in the dynamic case
Alicia Arjona, Jesus Ildefonso Diaz
Abstract:
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 viscoelasticgravitational displacements
resulting from body forces embedded in a layered Earth model leads to a
wellposed problem even for any kind of domains, with the natural boundary
and transmission conditions. A homogeneous or stratified viscoelastic
halfspace 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 viscoelasticgravitational field equations.
Published November 20, 2015.
Math Subject Classifications: 35K10, 35L10, 35Q86, 35Q74, 46E35, 86A60.
Key Words: Gravity changes; viscoelasticgravitational 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, L7256 Walferdange
GranDuchy 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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