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• W4380788835 abstract "Abstract In this paper, we study the initial boundary value problem for the nonlocal parabolic equation with the Hardy–Littlewood–Sobolev critical exponent on a bounded domain. We are concerned with the long time behaviors of solutions when the initial energy is low, critical or high. More precisely, by using the modified potential well method, we obtain global existence and blow-up of solutions when the initial energy is low or critical, and it is proved that the global solutions are classical. Moreover, we obtain an upper bound of blow-up time for $$J_{mu }(u_{0})<0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>u</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and decay rate of $$H^{1}_{0}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> <mml:mn>1</mml:mn> </mml:msubsup> </mml:math> and $$L^{2}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -norm of the global solutions. When the initial energy is high, we derive some sufficient conditions for global existence and blow-up of solutions. In addition, we are going to consider the asymptotic behavior of global solutions, which is similar to the Palais-Smale (PS for short) sequence of stationary equation." @default.
• W4380788835 created "2023-06-16" @default.
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• W4380788835 date "2023-06-15" @default.
• W4380788835 modified "2023-10-05" @default.
• W4380788835 title "Global Existence and Blow-up Solutions for a Parabolic Equation with Critical Nonlocal Interactions" @default.
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• W4380788835 doi "https://doi.org/10.1007/s10884-023-10278-y" @default.
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