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Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity

Filippas, Stathis and Herrero, Miguel A. and Velázquez, J.J. L. (2000) Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 456 . pp. 2957-2982. ISSN 1364-5021

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Matched asymptotic expansions; semilinear heat equation; blow-up; critical exponents; singularities; dynamics
Subjects:Sciences > Mathematics > Differential equations
ID Code:16657
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