| 带有变指标反应项的非线性抛物方程的爆破 |
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| 引用本文： | 宋士勤,唐树乔.带有变指标反应项的非线性抛物方程的爆破[J].长春大学学报,2012(2):170-172. |
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| 作者姓名： | 宋士勤 唐树乔 |
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| 作者单位： | 亳州师范高等专科学校理化系;安徽大学数学科学学院;东南大学数学系 |
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| 基金项目： | 安徽省自然科学基金(KJ2011z258);毫州师范高等专科学校教学教育专业(省级特色专业);江苏省基础研究计划(自然科学基金)面上项目(BK2010404) |
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| 摘 要： | 研究了具有齐次Dirichlet边界和变指标反应项的非线性抛物方程ut=Δu+a|u|p(x)(a0)在(x,t)∈Ω×(0,T)(T0)内非负解的爆破性质,并运用特征函数方法得到方程解在有限时刻爆破的条件。
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| 关 键 词： | 变指标 梯度项 非线性抛物方程 特征函数方法 爆破 |
Blow-up for a Nonlinear Parabolic Equation with Variable Reactions |
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| SONG Shi-qin,TANG Shu-qiao.Blow-up for a Nonlinear Parabolic Equation with Variable Reactions[J].Journal of Changchun University,2012(2):170-172. |
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| Authors: | SONG Shi-qin TANG Shu-qiao |
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| Institution: | 1,3(1.Department of Science,Bozhou Teachers College,Bozhou 236800,China; 2.School of Mathematics Science,Anhui University,Hefei 230039,China; 3.Department of Mathematics,Southeast University,Nanjing 211100,China) |
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| Abstract: | This paper studies the blow-up property of non-negative solutions to the nonlinear parabolic equation ut=Δu+a|u|p(x)(a>0)在(x,t)∈Ω×(0,T)(T>0) with homogeneous Dirichlet boundary conditions and variable reaction in(x,t)∈Ω×(0,T)(T>0),and obtains the condition of blow-up at a finite time by using eigenfunction method. |
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| Keywords: | variable index gradient term nonlinear parabolic equation eigenfunction method blow-up |
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