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• W1559907623 abstract "Consider an evolutionary equation related to the $p(x)$ -Laplacian: ${u_{t}}= operatorname{div} ({rho^{alpha}}{ vert {nabla u} vert ^{p(x) - 2}}nabla u)+ {frac{{partial{b_{i}}(u,x,t)}}{{partial {x_{i}}}}}$ , $(x,t) in{Q_{T}} = Omega times(0,T)$ , which arises from electrorheological fluid mechanics. Since $rho(x) = operatorname{dist} (x,partialOmega)$ , the equation is degenerate on the boundary, one may expect that there is not flux across the boundary. The paper shows that the facts may be unexpected. The paper reviews Fichera-Oleinik theory, then uses the theory to discuss the boundary value condition related to the equation. If $p^{-}>2$ , the existence and the uniqueness of the solutions are researched. Finally, if $b_{i}equiv0$ , the behavior of the solutions near the boundary is studied by the comparison theorem." @default.
• W1559907623 created "2016-06-24" @default.
• W1559907623 creator A5048331270 @default.
• W1559907623 date "2015-07-02" @default.
• W1559907623 modified "2023-10-18" @default.
• W1559907623 title "The boundary value condition of an evolutionary p ( x ) $p(x)$ -Laplacian equation" @default.
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• W1559907623 doi "https://doi.org/10.1186/s13661-015-0377-6" @default.
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