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Blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions. (English) Zbl 1148.35040

Summary: We give a positive answer to the conjecture proposed in [A. El Soufi, M. Jazar and R. Monneau, Ann. Inst. Henri Poincaré Anal. Non Linéaire 24, No. 1, 17–39 (2007; Zbl 1112.35108)] concerning the finite time blow-up for solutions of the problem

u t -Δu=|u| p - Ω |u| p inΩ

with homogeneous Neumann boundary conditions.

35K60Nonlinear initial value problems for linear parabolic equations
45K05Integro-partial differential equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)