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Mathematical Analysis of a Model of River Channel Formation

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Díaz Díaz, Jesús Ildefonso y Fowler, A.C. y Muñoz, Ana Isabel y Schiavi, E. (2008) Mathematical Analysis of a Model of River Channel Formation. Pure and Applied Geophysics, 165 (8). pp. 1663-1682. ISSN 0033-4553

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URL Oficial: http://www.springerlink.com/content/k130385n2109476k/


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Resumen

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin.


Tipo de documento:Artículo
Palabras clave:drainage-basin evolution; driven theory; stability; inception; equation; river models; landscape evolution; nonlinear parabolic equations; free boundaries; singular free boundary flux
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:15177
Depositado:10 May 2012 08:28
Última Modificación:06 Feb 2014 10:18

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