Existence of solutions to an initial Dirichlet problem of evolutional p(x)-Laplace equations
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 3, p. 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 : https://doi.org/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},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     pages = {377-399},
     doi = {10.1016/j.anihpc.2012.01.001},
     zbl = {1255.35153},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 29 (2012) no. 3, pp. 377-399. doi : 10.1016/j.anihpc.2012.01.001. http://www.numdam.org/item/AIHPC_2012__29_3_377_0/

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