Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems

Juraj Földes

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 1, page 169-198
  • ISSN: 0011-4642

Abstract

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In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.

How to cite

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Földes, Juraj. "Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems." Czechoslovak Mathematical Journal 61.1 (2011): 169-198. <http://eudml.org/doc/196953>.

@article{Földes2011,
abstract = {In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.},
author = {Földes, Juraj},
journal = {Czechoslovak Mathematical Journal},
keywords = {a priori estimates; Liouville theorems; blow-up rate; positive solution; indefinite parabolic problem; a priori estimate; Liouville theorem; blow-up rate; positive solution; indefinite parabolic problem},
language = {eng},
number = {1},
pages = {169-198},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems},
url = {http://eudml.org/doc/196953},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Földes, Juraj
TI - Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 1
SP - 169
EP - 198
AB - In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.
LA - eng
KW - a priori estimates; Liouville theorems; blow-up rate; positive solution; indefinite parabolic problem; a priori estimate; Liouville theorem; blow-up rate; positive solution; indefinite parabolic problem
UR - http://eudml.org/doc/196953
ER -

References

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