Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
نویسندگان
چکیده
We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation ut = ∆u + |u|p−1u. 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 timeperiodic solutions are also shown. ∗Corresponding author. †Supported in part by DFG grant GI 30/82-1.
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