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Consider the anisotropic parabolic equation with the variable exponent ut=∑i=1N(ai(x)|uxi|pi(x)−2uxi)xi,$$ {u_{t}}=\sum_{i=1}^{N} \bigl(a_{i}(x)|u_{x_{i}}|^{p_{i}(x)-2}u_{x_{i}} \bigr)_{x _{i}}, $$ with ai(x)$a_{i}(x)$, pi(x)∈C1(Ω‾)$p_{i}(x)\in C^{1}(\overline{\Omega})$, pi(x)>1$p_{i}(x)>1$, ai(x)≥0$a_{i}(x)\geq0$. If some of {ai(x)}$\{a_{i}(x)\}$ are degenerate on the boundary,… Click to show full abstract
Consider the anisotropic parabolic equation with the variable exponent ut=∑i=1N(ai(x)|uxi|pi(x)−2uxi)xi,$$ {u_{t}}=\sum_{i=1}^{N} \bigl(a_{i}(x)|u_{x_{i}}|^{p_{i}(x)-2}u_{x_{i}} \bigr)_{x _{i}}, $$ with ai(x)$a_{i}(x)$, pi(x)∈C1(Ω‾)$p_{i}(x)\in C^{1}(\overline{\Omega})$, pi(x)>1$p_{i}(x)>1$, ai(x)≥0$a_{i}(x)\geq0$. If some of {ai(x)}$\{a_{i}(x)\}$ are degenerate on the boundary, a partial boundary value condition is imposed, the stability of weak solutions can be proved based on the partial boundary value condition.
Journal Title: Boundary Value Problems
Year Published: 2017
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