on the blow-up set for non-newtonian equation with a nonlinear boundary condition

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2010
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Abstract
We identify the blow-up set of solutions to the problem ๐‘ข๐‘ก=(|๐‘ข๐‘ฅ|๐‘โˆ’2๐‘ข๐‘ฅ)๐‘ฅ, ๐‘ฅ>0, ๐‘กโˆˆ(0,๐‘‡), โˆ’|๐‘ข๐‘ฅ|๐‘โˆ’2๐‘ข๐‘ฅ(0,๐‘ก)=๐‘ข๐‘โˆ’1(0,๐‘ก), ๐‘กโˆˆ(0,๐‘‡), and ๐‘ข(๐‘ฅ,0)=๐‘ข0(๐‘ฅ)โ‰ฅ0, ๐‘ฅ>0, where ๐‘>2. We obtain that the blow up set ๐ต(๐‘ข) satisfies [0,๐‘(๐‘โˆ’1)/(๐‘โˆ’2))โŠ‚๐ต(๐‘ข)โŠ‚[0,๐‘(๐‘โˆ’1)/(๐‘โˆ’2)]. The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.
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Authors Zhilei Liang
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Journal science and technology of advanced materials
Year 2010
DOI
10.1155/2010/680572
URL
http://dx.doi.org/10.1155/2010/680572
Keywords
mathematics

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