Geodesic
Existence of solutions to a parabolic \(p(x)\)-Laplace equation with convection term via \(L^{\infty}\)-infinity estimates
Electronic journal of differential equations, Tome 2015 (2015)
This article is devoted to the study of the existence of weak solutions to an initial and boundary value problem for a parabolic $p(x)$-Laplace equation with convection term. Using the De Giorgi iteration technique, the authors establish the critical a priori L-infinity estimates and thus prove the existence of weak solutions.
Classification : 35K65, 35K55, 46E35
Keywords: parabolic $p(x)$-Laplace equation, convection term, de giorgi iteration, L-infinity estimates 
@article{EJDE_2015__2015__a31,
     author = {Li,  Zhongqing and Yan,  Baisheng and Gao,  Wenjie},
     title = {Existence of solutions to a parabolic {\(p(x)\)-Laplace} equation with convection term via {\(L^{\infty}\)-infinity} estimates},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1515.35152},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a31/}
}
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%J Electronic journal of differential equations
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%F EJDE_2015__2015__a31
Li,  Zhongqing; Yan,  Baisheng; Gao,  Wenjie. Existence of solutions to a parabolic \(p(x)\)-Laplace equation with convection term via \(L^{\infty}\)-infinity estimates. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a31/