Open AccessGlobal existence and blow-up for semilinear parabolic equation with critical exponent in R N
Author(s) -
Fei Fang,
Binlin Zhang
Publication year - 2022
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2022.1.3
Subject(s) - algorithm , exponent , sobolev space , mathematics , norm (philosophy) , energy (signal processing) , computer science , mathematical analysis , statistics , law , philosophy , linguistics , political science
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 R N . 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].