On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition

Zhilei Liang

Abstract and Applied Analysis, 2010, vol. 2010, 1-12

Abstract:

We identify the blow-up set of solutions to the problem ð ‘¢ ð ‘¡ = ( | ð ‘¢ ð ‘¥ | ð ‘ âˆ’ 2 ð ‘¢ ð ‘¥ ) ð ‘¥ , ð ‘¥ > 0 , ð ‘¡ ∈ ( 0 , 𠑇 ) , − | ð ‘¢ ð ‘¥ | ð ‘ âˆ’ 2 ð ‘¢ ð ‘¥ ( 0 , ð ‘¡ ) = ð ‘¢ ð ‘ âˆ’ 1 ( 0 , ð ‘¡ ) , ð ‘¡ ∈ ( 0 , 𠑇 ) , and ð ‘¢ ( ð ‘¥ , 0 ) = ð ‘¢ 0 ( ð ‘¥ ) ≥ 0 , ð ‘¥ > 0 , where ð ‘ > 2 . We obtain that the blow up set ð µ ( ð ‘¢ ) satisfies [ 0 , ð ‘ ( ð ‘ âˆ’ 1 ) / ( ð ‘ âˆ’ 2 ) ) ⊂ ð µ ( ð ‘¢ ) ⊂ [ 0 , ð ‘ ( ð ‘ âˆ’ 1 ) / ( ð ‘ âˆ’ 2 ) ] . The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:680572

DOI: 10.1155/2010/680572

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