Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Sobre el problema inverso de difusión
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Keywords

inverse problems
group analysis of differential equations
similarity
fractals
diffusion
porous medium
Problemas inversos
análisis de grupo de ecuaciones diferenciales
similaridad
fractales
difusión
medios porosos

How to Cite

Mercado E., J. R., Aldama R., Á. A., & Brambila P., F. (2003). Sobre el problema inverso de difusión. Revista De Matemática: Teoría Y Aplicaciones, 10(1-2), 92–105. https://doi.org/10.15517/rmta.v10i1-2.226

Abstract

Infiltration is physically described in order to model it as a diffusion stochastic process. Theorem M-B 1 is enunciated; whose main objective is the inverse diffusion problem. The theorem is demonstrated in the specific context of solution injectability, and it is applied to solve the inverse diffusion problem in the presence of Boltzmann’s group. The inverse problem of the similarity exponent is solved following group analysis methods. The dispersion of a water drop in a three-dimensional porous medium is applied; a result which in turn is applicable to drop irrigation.

https://doi.org/10.15517/rmta.v10i1-2.226
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References

Bluman, G.W.; Kumei, S. (1989) Symmetries and Differential Equations. Springer-Verlag, New York.

Broadbridge, P.; Goard, J.M.; Lavrentiev Jr., M. (1997) “Degenerate nonlinear difussion with an initially sharp front”, Studies in Applied Math. 99: 377–391.

Colton, D.; Ewing, R.; Rundell, W. (Eds.) (1990) Inverse Problems in Partial Differential Equations. SIAM, Philadelphia.

Doob, J.L. (1960) Stochastic Processes. John Wiley & Sons, New York.

Galaktionov, V.A. (1994) “Blow-up for quasilinear heat equations with critical Fujita’s exponents”, Proceedings of the Royal Society of Edinburgh 124A: 517–525.

Mercado, J.R.; Aldama, Á.A.; Brambila, F. (2002) “Sobre la ecuación de Boussinesq del medio poroso”, Aportaciones Matemáticas, Serie Comunicaciones 30: 165–187.

Mercado, J.R.; Brambila, F. (2001) “Problemas inversos en las ecuaciones de Fokker-Planck”, Aportaciones Matemáticas, Serie Comunicaciones 29: 201–222.

Mercado, J.R.; Hernández, G.; Ramos, L.J.; Ockendon, H.; Brambila, F. (1999) “Problemas directo e inverso para el abatimiento del manto freático”, Aportaciones Matemáticas 23: 49–58.

Mercado, J.R.; Namuche, R.; Fuentes, C.; Brambila, F. (1996) “Naturaleza fractal de la difusividad hidráulica”, XVII Congreso Latinoamericano de Hidráulica, Guayaquil, Ecuador.

Oksendal, B. (1989) Stochastic Differential Equations. Springer-Verlag, New York.

Olver, P.J. (1993) Applications Lie Groups to Differential Equations. Springer-Verlag, Berlin.

Pattle; R. E. (1959) “Difusion from an instantaneous point source with a concentration-dependent coefficient”, Quart. Journ. Mech. and Appl. Math. 12(4): 407–409.

Philip, J.R. (1960) “General method of exact solution of the concentration-dependent diffusion equation”, Austral. J. Phys. 13: 1–12.

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