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Zbl 1176.35010
Cazenave, Thierry; Dickstein, Flávio; Weissler, Fred B.
Global existence and blowup for sign-changing solutions of the nonlinear heat equation.
(English)
[J] J. Differ. Equations 246, No. 7, 2669-2680 (2009). ISSN 0022-0396

Given $0<\alpha<2/N$, it is proved that a function $\psi$ exists with the following properties: The solution of the equation $u_t+\Delta u=|u|^\alpha u$ in $\bbfR^N$ with the initial condition $\psi$ is global while the solution with the initial condition $\lambda\psi$ blows up in finite time if $\lambda >0$ is either sufficiently small or sufficiently large.
[Chiu Yeung Chan (Lafayette)]
MSC 2000:
*35B05 General behavior of solutions of PDE
35K55 Nonlinear parabolic equations
35B35 Stability of solutions of PDE
35K57 Reaction-diffusion equations
35K15 Second order parabolic equations, initial value problems

Keywords: finite-time blowup; semilinear equation

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