| Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries |
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| 作者姓名： | Ling-hua KONG~ |
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| 作者单位： | Ling-hua KONG~(1 ) Ming-xin WANG~(2，3) 1 Department of Applied Mathematics，Dalian University of Technology，Dalian 116024，China; 2 Department of Mathematics，Southeast University，Nanjing 210018，China; 3 Department of Mathematics，Xuzhou Normal University，Xuzhou 221116，China |
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| 摘 要： | This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.
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Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries |
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| Ling-hua KONG.Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries[J].Science in China(Mathematics),2007,50(9):1251-1266. |
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| Authors: | Ling-hua Kong Ming-xin Wang |
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| Institution: | 1. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China
2. Department of Mathematics, Southeast University, Nanjing 210018, China;Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China |
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| Abstract: | This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented. |
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| Keywords: | parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile |
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