On theBlow‐UpSet for Non‐Newtonian Equation with a Nonlinear Boundary Condition

Zhilei Liang

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: We identify the blow‐up set of solutions to the problem ut = (|ux|p−2ux) x, x > 0, t ∈ (0, T), −|ux|p−2ux(0, t) = up−1(0, t), t ∈ (0, T), and u(x, 0) = u0(x) ≥ 0, x > 0, where p > 2. We obtain that the blow up set B(u) satisfies [0, p(p − 1)/(p − 2)) ⊂ B(u)⊂[0, p(p − 1)/(p − 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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https://doi.org/10.1155/2010/680572

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:680572

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