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Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations

Thomas BartschPeter PoláčikPavol Quittner — 2011

Journal of the European Mathematical Society

We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation u t = 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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