Global existence and blow-up for semilinear parabolic equation with critical exponent in RN

Fang Fei and Zhang Binlin: Global existence and blow-up for semilinear parabolic equation with critical exponent in RN. (2022)

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Abstract

In this paper, we use the self-similar transformation and the modified potential well method to study the long time behaviors of solutions to the classical semilinear parabolic equation associated with critical Sobolev exponent in RN. Global existence and finite time blowup of solutions are proved when the initial energy is in three cases. When the initial energy is low or critical, we not only give a threshold result for the global existence and blowup of solutions, but also obtain the decay rate of the L 2 norm for global solutions. When the initial energy is high, sufficient conditions for the global existence and blowup of solutions are also provided. We extend the recent results which were obtained in [R. Ikehata, M. Ishiwata, T. Suzuki, Ann. Inst. H. Poincaré Anal. Non Linéaire 27(2010), No. 3, 877– 900].

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 3
ISSN: 1417-3875
Number of Pages: 23
Language: English
Place of Publication: Szeged
DOI: 10.14232/ejqtde.2022.1.3
Uncontrolled Keywords: Differenciálegyenlet - parabolikus
Additional Information: Bibliogr.: p. 21-23. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. May. 23. 15:00
Last Modified: 2022. May. 24. 08:15
URI: http://acta.bibl.u-szeged.hu/id/eprint/75818

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