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Global existence and blowup for sign-changing solutions of the nonlinear heat equation. (English) Zbl 1176.35010
Given 0<α<2/N, it is proved that a function ψ exists with the following properties: The solution of the equation u t +Δu=|u| α u in N with the initial condition ψ is global while the solution with the initial condition λψ blows up in finite time if λ>0 is either sufficiently small or sufficiently large.
MSC:
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
References:
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