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

Díaz, 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 -