Publication: Geometric form of volcanoes with a limited based
Loading...
Files
Official URL
Full text at PDC
Publication Date
2009
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad de Castilla-La Mancha
Citations
Exportar
Abstract
Many volcanic constructs have geometric different shapes depending on different phenomena as parasitic cones, erosion or coral growth. In Lacey, Ockendon and Turcotte [11] the authors proposed a nonlinear model proving that the shape of volcanoes is determined by the hydraulic resistance to the flow of magma, from a line source, through the porous edifice. This model was later extended in Angevine, Turcotte and Ockendon [2] to include the shape of aseismic, submarine ridges. In this communication we propose a modification of the above mentioned models in order to simulate the more realistic case of volcanoes with a limited base.
Description
XXI Congreso de Ecuaciones Diferenciales y Aplicaciones
XI Congreso de Matematica Aplicada, Ciudad Real, 21-25 septiembre 2009
UCM subjects
Unesco subjects
Keywords
Citation
Alt, H. W. and Luckhaus, S., Quasilinear elliptic-parabolic differential equations, Math. Z., 183, pp. 311–341, 1983.
Angevine, C.L., Turcotte, D.L., Ockendon, J.R., Geometrical form of aseismic ridges,volcanoes and seamounts, Journal of Geophysical Resarch, 89, 11, 287-292, 1984.
Antontsev, S., Díaz, J. I., Shmarev, S., Energy methods for free boundary problems. Applications to nonlinear PDEs and Fluid Mechanics, Series Progress in Nonlinear Differential Equations and Their Applications, No. 48, Birkäuser, Boston, 2002.
Ph. Benilan, J. I. Díaz, Pointwise gradient estimates of solutions of onedimensional nonlinear parabolic problems, J. Evolution Equations, 3, 557-602, 2004.
Díaz, J. I., Qualitative Study of Nonlinear Parabolic Equations: an Introduction, Extracta Mathematicae, 16, núm.2, 303-341, 2001.
Díaz, J. I., Kersner,R. , On a nonlinear degenerate parabolic equation in filtration or evaporation through a porous medium. Journal of Differential Equations, Vol 69, No 3, 368- 403, 1987.
Díaz, J.I., Kersner, R., On the behaviour and cases of nonexistence of the free boundary in a semibounded porous medium, Journal of Mathematical Analysis and Application, Vol 132, No 1, 281 289, 1988.
Díaz, J. I. and Shmarev, S. I., On the behaviour of the interface in nonlinear processes with convection dominating diffusion via Lagrangian coordinates. Advances in Mathematical Sciences and Applications, Vol 1, No1, 19 45, 1992.
Gilding, B. H. Improved theory for a nonlinear degenerate parabolic equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, S´er. 4, 16 no. 2, p. 165-224, 1989.
Kalashnikov, A.S., Some problems of qualitative theory of nonlinear degenerate second-order parabolic equations, Uspekhi Mat. Nauk., 42, 135-176, 1987.
Lacey, A., Ockendon, J.R., Turcotte, D.L., On the geometrical form of volcanoes, Earth Planet.Sci.Lett., 54, 139-143, 1981.