On regular metric trees, KPP solutions propagate if f'(0) > E0 and become extinct if f'(0) < E0 (homogeneous case), with speed estimates between 2*sqrt(f'(0)-E0) and M*rho1*b1/(b1-1).
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Extinction and propagation phenomena for semilinear parabolic equations on metric trees
On regular metric trees, KPP solutions propagate if f'(0) > E0 and become extinct if f'(0) < E0 (homogeneous case), with speed estimates between 2*sqrt(f'(0)-E0) and M*rho1*b1/(b1-1).