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Global existence and blowup for sign-changing solutions of the nonlinear heat equation |
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| Authors: | Thierry Cazenave Flávio Dickstein Fred B Weissler |
| Institution: | a UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France b CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France c Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21944-970 Rio de Janeiro, RJ, Brazil d Université Paris 13, LAGA UMR CNRS 7539, 99 Avenue J.-B. Clément, 93430 Villetaneuse, France |
| Abstract: | In this paper, given 0<α<2/N, we prove the existence of a function ψ with the following properties. The solution of the equation ut−Δu=α|u|u on RN with the initial condition u(0)=ψ is global. On the other hand, the solution with the initial condition u(0)=λψ blows up in finite time if λ>0 is either sufficiently small or sufficiently large. |
| Keywords: | 35K55 35B35 |
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