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

Thomas Bartsch; Peter Poláčik; Pavol Quittner

Journal of the European Mathematical Society (2011)

- Volume: 013, Issue: 1, page 219-247
- ISSN: 1435-9855

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topBartsch, 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 -

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