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.

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
Mots-clés : Electrorheological fluids, $ p(x)$-Laplace, Degenerate, Parabolic 
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     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},
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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. http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.001/

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