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 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 |
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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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