Título:
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The mesa problem: diffusion patterns for ut=??(um?u) as m?+?
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Autores:
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Elliot, C. M. ;
Herrero, Miguel A. ;
King, J. R. ;
Ockendon, J.R.
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Tipo de documento:
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texto impreso
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Editorial:
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Oxford University Press, 1986
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Ecuaciones diferenciales
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Tipo = Artículo
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Resumen:
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In this paper we consider the limit m?+? of solutions of the porous-medium equation ut = ?•(um?u)(x?RN), with N > 1. We conjecture that, for initial data with a unique maximum, the evolution is characterized by the onset of a ‘mesa’ region, in which the solution is nearly spatially independent, surrounded by a region in which u is nearly equal to its initial value. The transition between these regions occurs near a surface which is identified with the free boundary in a certain Stefan problem which can be studied using variational inequalities. Moreover, singular-perturbation theory can be used to describe the structure of the transition region.
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