Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
Thomas BartschUniversität Giessen, Germany
Peter PolacikUniversity of Minnesota, Minneapolis, United States
Pavol QuittnerComenius University, Bratislava, Slovak Republic
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. 219–247DOI 10.4171/JEMS/250