| 一类具有局部化源和吸收项的抛物系统解的整体存在与爆破 |
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| 引用本文： | 周军.一类具有局部化源和吸收项的抛物系统解的整体存在与爆破[J].数学学报,2013(1):67-86. |
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| 作者姓名： | 周军 |
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| 作者单位： | 西南大学数学与统计学院 |
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| 基金项目： | 国家自然科学数学天元基金(11126141);国家自然科学青年基金(11201380);中央高校基本科研业务费重点项目(XDJK2012B007);西南大学博士基金(SWU111021);西南大学教育基金(2010JY053) |
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| 摘 要： | 在齐次Dirichlet边界条件研究如下抛物系统其中x_0(t):R+→(0,a)是Holder连续函数;常数0≤α,β<1,p_1,p_2,q_1,q_2,k_1,k_2>0.利用正则化方法,在一定的假设条件下证明了经典解的存在性.接着利用比较原理证明了该系统正解的整体存在性和爆破性.最后给出了爆破解的精确爆破速率和爆破模式.
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| 关 键 词： | 退化奇异抛物系统 整体存在 爆破速率 爆破模式 |
Global Existence and Blow-up Properties for a Parabolic System with Localized Source and Absorption |
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| Jun ZHOU.Global Existence and Blow-up Properties for a Parabolic System with Localized Source and Absorption[J].Acta Mathematica Sinica,2013(1):67-86. |
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| Authors: | Jun ZHOU |
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| Institution: | Jun ZHOU School of Mathematics and Statistics,Southwest University, Chongqing 400715,P.R.China |
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| Abstract: | The aim of this paper is to investigate the following parabolic system under homogeneous Dirichlet boundary condition,where x_0(t):R~+→(0,a) is Holder continuous,and the constants 0≤α,β< 1,p_1,p_2,q_1,q_2,k_1,k_2 > 0.Under appropriate hypotheses,we first prove the local existence of classical solution by a regularization method.Then we discuss the global existence and blow-up of positive solutions by using a comparison principle.Finally,we give the precise blow-up estimates and the uniform blow-up profiles. |
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| Keywords: | degenerate and singular parabolic system global existence blow-up rate uniform blow-up profiles |
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