JournalsjemsVol. 13, No. 1pp. 219–247

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

  • Thomas Bartsch

    Universität Giessen, Germany
  • Peter Polacik

    University of Minnesota, Minneapolis, United States
  • Pavol Quittner

    Comenius University, Bratislava, Slovak Republic
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations cover
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Abstract

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.

Cite this article

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. 219–247

DOI 10.4171/JEMS/250