Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.

Título inglés Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.
Título español Unicidad y existencia de la solución en el espacio BVt(Q) de un problema parabólico doblemente no lineal.
Autor/es Díaz, Jesús Ildefonso ; Padial, Juan Francisco
Organización Dep. Mat. Apl. Fac. Mat. Univ. Complut. Madrid, Madrid, España; Esc. Téc. Super. Arquit. Univ. Politéc. Madrid, Madrid, España
Revista 0214-1493
Publicación 1996, 40 (2): 527-560, 28 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equation
b(u)t - div (|Ñu - k(b(u))e|p-2 (Ñu - k(b(u))e)) + g(x,u) = f(t,x).
This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines, etc. The solvability of this problem is established in the BVt(Q) space. We prove some comparison properties (implying uniqueness) when the set of jumping points of the BV solution has N-dimensional null measure and suitable additional conditions as, for instance, b-1 locally Lipschitz. The existence of this type of weak solution is based on suitable uniform estimates of the BV norm of an approximated solution.
Clasificación UNESCO 120203 ; 121009
Palabras clave español Problema de Cauchy ; Problema de Dirichlet ; Ecuaciones no lineales ; Ecuaciones parabólicas ; Espacios de Banach ; Funciones de variación acotada ; Distancia de Hausdorff ; Solución débil ; Unicidad
Código MathReviews MR1425634
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