Abstract.
This paper is concerned with where Ω is a bounded smooth domain in R N, T D >0, D>0, and p>1 with (N−2)p≤N+2. Let P 2 be the projection from L 2(Ω) onto the second Neumann eigenspace. We prove that, if P 2φ≠0 in Ω and D is sufficiently large, the solution u of (P) blows up only near the set ℳ∪∂Ω, where \({{{{\cal{ M}}}=\{x\in\overline{{\Omega}}:(P_2 \phi)(x) =\max_{{y\in\overline{{\Omega}}}}(P_2 \phi)(y)\}}}\).
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Mathematics Subject Classification (2000): 35K20, 35K55, 58K57
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Ishige, K., Mizoguchi, N. Location of blow-up set for a semilinear parabolic equation with large diffusion. Math. Ann. 327, 487–511 (2003). https://doi.org/10.1007/s00208-003-0463-4
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DOI: https://doi.org/10.1007/s00208-003-0463-4