The well-posedness of an anisotropic parabolic equation based on the partial boundary value condition
Abstract Consider the anisotropic parabolic equation with the variable exponent u t = ∑ i = 1 N ( a i ( x ) | u x i | p i ( x ) − 2 u x i ) x i , $$ {u_{t}}=\sum_{i=1}^{N} \bigl(a_{i}(x)|u_{x_{i}}|^{p_{i}(x)-2}u_{x_{i}} \bigr)_{x _{i}}, $$ with a i ( x ) $a_{i}(x)$ , p i ( x ) ∈ C 1 ( Ω ‾ ) $p_{i}(x...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-11-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0899-1 |