%0 Journal Article
%A Filippas, Stathis
%A Herrero, Miguel A.
%A Velázquez, J.J. L.
%T Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
%D 2000
%@ 1364-5021
%U https://hdl.handle.net/20.500.14352/57582
%X We consider the semilinear heat equation with critical power nonlinearity. Using formal. arguments based on matched asymptotic expansion techniques, we give a detailed description of radially symmetric sign-changing solutions, which blow-up at x = 0 and t = T < ∞, for space dimension N = 3,4,5,6. These solutions exhibit fast blow-up; i.e. they satisfy lim(t up arrowT)(T - t)(1/(p-1))u(0, t) = ∞. In contrast, radial solutions that are positive and decreasing behave as in the subcritical case for any N ≥ 3. This last result is extended in the case of exponential nonlinearity and N = 2.
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