Geodesic
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 219-247

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/250
Classification : 35-XX, 00-XX
Keywords: Semilinear parabolic equations, Liouville theorems, nodal radial solutions, a priori estimates, blow-up rate, decay rate, periodic solutions 
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     title = {Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations},
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Thomas Bartsch; Peter Polacik; Pavol Quittner. Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations. Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 219-247. doi: 10.4171/jems/250

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