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

Bartsch, Thomas, Poláčik, Peter, and Quittner, Pavol. "Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations." Journal of the European Mathematical Society 013.1 (2011): 219-247. <http://eudml.org/doc/277360>.

@article{Bartsch2011,
abstract = {We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation $u_t=\Delta u+\left|u\right|^\{p-1\}u$. 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.},
author = {Bartsch, Thomas, Poláčik, Peter, Quittner, Pavol},
journal = {Journal of the European Mathematical Society},
keywords = {semilinear parabolic equations; Liouville theorems; nodal radial solutions; a priori estimates; blow-up rate; decay rate; periodic solutions; nonexistence results; a priori bounds; sign-changing solutions; nonexistence results; a priori bounds; blow up rate; decay rate; periodic orbits; nodal radial solutions; sign-changing solutions},
language = {eng},
number = {1},
pages = {219-247},
publisher = {European Mathematical Society Publishing House},
title = {Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations},
url = {http://eudml.org/doc/277360},
volume = {013},
year = {2011},
}

TY - JOUR
AU - Bartsch, Thomas
AU - Poláčik, Peter
AU - Quittner, Pavol
TI - Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
JO - Journal of the European Mathematical Society
PY - 2011
PB - European Mathematical Society Publishing House
VL - 013
IS - 1
SP - 219
EP - 247
AB - We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation $u_t=\Delta u+\left|u\right|^{p-1}u$. 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.
LA - eng
KW - semilinear parabolic equations; Liouville theorems; nodal radial solutions; a priori estimates; blow-up rate; decay rate; periodic solutions; nonexistence results; a priori bounds; sign-changing solutions; nonexistence results; a priori bounds; blow up rate; decay rate; periodic orbits; nodal radial solutions; sign-changing solutions
UR - http://eudml.org/doc/277360
ER -