Geometrical evolution of volcanoes: a theoretical approach

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Abstract

Shape of many volcanic edifices depend on different phenomena, such as parasitic cones, erosion or coral growth. A nonlinear model proposed in 1981 proves that the shape of volcanoes is determined by the hydraulic resistance to the flow of magma, along a line, through the porous edifice. This model was later extended to include the shape of aseismic and submarine ridges. In this paper we propose a modification of the above mentioned models in order to simulate the more realistic case of volcanoes growth assuming they have a limited base. We present the 3D extension and a generalization of the model. We formulate a new model including the case of a possible outpointing flow.

Keywords

Geometric of volcanoes Limited base Degenerate parabolic equation Bounded free boundary 

Mathematics Subject Classification

76S05 35K55 35R35 
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Notes

Acknowledgments

The authors thank Professor J. Fernández for several useful conversations on this subject and to the two anonymous referees for their careful reading of the manuscript. The research of A. Arjona was supported by the National Research Fund of Luxembourg (AFR Grant 4832278). The research of J. I. Díaz was partially supported by the project ref. MTM2011-26119 of the DGISPI (Spain) and the Research Group MOMAT (Ref. 910480) supported by UCM. He has received also support from the ITN FIRST of the Seventh Framework Program of the European Community’s (Grant Agreement Number 238702).

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Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  1. 1.European Center for Geodynamics and SeismologyWalferdangeGrand Duchy of Luxembourg
  2. 2.Departamento de Matemática Aplicada, Instituto de Matematica Interdisciplinar yFacultad de MatemáticasMadridSpain

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