Geodesic
Existence of solutions to an initial Dirichlet problem of evolutional p(x)-Laplace equations
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 377-399

Voir la notice de l'article provenant de la source Numdam

The existence and uniqueness of weak solutions are studied to the initial Dirichlet problem of the equation

u t = div |∇u| p(x)-2 ∇u+f(x,t,u),
with inf p(x)>2. The problems describe the motion of generalized Newtonian fluids which were studied by some other authors in which the exponent p was required to satisfy a logarithmic Hölder continuity condition. The authors in this paper use a difference scheme to transform the parabolic problem to a sequence of elliptic problems and then obtain the existence of solutions with less constraint to p(x). The uniqueness is also proved.

DOI : 10.1016/j.anihpc.2012.01.001
Keywords: Electrorheological fluids, $ p(x)$-Laplace, Degenerate, Parabolic 
@article{AIHPC_2012__29_3_377_0,
     author = {Lian, Songzhe and Gao, Wenjie and Yuan, Hongjun and Cao, Chunling},
     title = {Existence of solutions to an initial {Dirichlet} problem of evolutional $ p(x)${-Laplace} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {377--399},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     doi = {10.1016/j.anihpc.2012.01.001},
     zbl = {1255.35153},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.01.001/}
}
TY  - JOUR
AU  - Lian, Songzhe
AU  - Gao, Wenjie
AU  - Yuan, Hongjun
AU  - Cao, Chunling
TI  - Existence of solutions to an initial Dirichlet problem of evolutional $ p(x)$-Laplace equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2012
SP  - 377
EP  - 399
VL  - 29
IS  - 3
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.01.001/
DO  - 10.1016/j.anihpc.2012.01.001
LA  - en
ID  - AIHPC_2012__29_3_377_0
ER  - 
%0 Journal Article
%A Lian, Songzhe
%A Gao, Wenjie
%A Yuan, Hongjun
%A Cao, Chunling
%T Existence of solutions to an initial Dirichlet problem of evolutional $ p(x)$-Laplace equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2012
%P 377-399
%V 29
%N 3
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2012.01.001/
%R 10.1016/j.anihpc.2012.01.001
%G en
%F AIHPC_2012__29_3_377_0
Lian, Songzhe; Gao, Wenjie; Yuan, Hongjun; Cao, Chunling. Existence of solutions to an initial Dirichlet problem of evolutional $ p(x)$-Laplace equations. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 377-399. doi: 10.1016/j.anihpc.2012.01.001

Cité par Sources :