We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation ut = Δ_u_+|u|p-1_u_. We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence of steady states and time-periodic solutions are also shown.
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Thomas Bartsch, Peter Polacik, Pavol Quittner, Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. J. Eur. Math. Soc. 13 (2011), no. 1, pp. 219–247DOI 10.4171/JEMS/250