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Global existence and blowup for sign-changing solutions of the nonlinear heat equation. (English) Zbl 1176.35010
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.

35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35K55Nonlinear parabolic equations
35B35Stability of solutions of PDE
35K57Reaction-diffusion equations
35K15Second order parabolic equations, initial value problems
Full Text: DOI
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