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

Jesús Ildefonso Díaz; Juan Francisco Padial

Publicacions Matemàtiques (1996)

- Volume: 40, Issue: 2, page 527-560
- ISSN: 0214-1493

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topDíaz, Jesús Ildefonso, and Padial, Juan Francisco. "Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.." Publicacions Matemàtiques 40.2 (1996): 527-560. <http://eudml.org/doc/41258>.

@article{Díaz1996,

abstract = {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 equationb(u)t - div (|∇u - k(b(u))e|p-2 (∇u - 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.},

author = {Díaz, Jesús Ildefonso, Padial, Juan Francisco},

journal = {Publicacions Matemàtiques},

keywords = {Problema de Cauchy; Problema de Dirichlet; Ecuaciones no lineales; Ecuaciones parabólicas; Espacios de Banach; Funciones de variación acotada; Distancia de Hausdorff; Solución débil; Unicidad; BV solutions; comparison properties},

language = {eng},

number = {2},

pages = {527-560},

title = {Uniqueness and existence of solution in the BVt(Q) space to a doubly nonlinear parabolic problem.},

url = {http://eudml.org/doc/41258},

volume = {40},

year = {1996},

}

TY - JOUR

AU - Díaz, Jesús Ildefonso

AU - Padial, Juan Francisco

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

JO - Publicacions Matemàtiques

PY - 1996

VL - 40

IS - 2

SP - 527

EP - 560

AB - 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 equationb(u)t - div (|∇u - k(b(u))e|p-2 (∇u - 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.

LA - eng

KW - Problema de Cauchy; Problema de Dirichlet; Ecuaciones no lineales; Ecuaciones parabólicas; Espacios de Banach; Funciones de variación acotada; Distancia de Hausdorff; Solución débil; Unicidad; BV solutions; comparison properties

UR - http://eudml.org/doc/41258

ER -

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