On theBlow‐UpSet for Non‐Newtonian Equation with a Nonlinear Boundary Condition
Zhilei Liang · Abstract and Applied Analysis · 2010
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.