非线性非局部边界条件的半线性耦合抛物型方程组

数学物理学报 ›› 2015, Vol. 35 ›› Issue (2): 234-244.

非线性非局部边界条件的半线性耦合抛物型方程组

凌征球, 覃思乾

玉林师范学院数学与信息科学学院广西玉林 537000

收稿日期:2014-04-25 修回日期:2015-01-22 出版日期:2015-04-25 发布日期:2015-04-25
作者简介:凌征球,E-mail:lingzq00@163.com
基金资助:
国家自然科学基金(11461076)和广西高校重点科研项目(ZD2014106)资助

Coupled Semilinear Parabolic System with Nonlinear Nonlocal Boundary Condition

Ling Zhengqiu, Qin Siqian

Institute of Mathematics and Information Science, Yulin Normal University, Guangxi Yulin 537000

Received:2014-04-25 Revised:2015-01-22 Online:2015-04-25 Published:2015-04-25

摘要/Abstract

摘要：

该文研究具有非负初始数据和非局部边界条件 u|∂Ω× (0,∞)=∫_Ωψ_i(x,y,t)u_i^l_i (y,t)dy 的半线性抛物型方程组 u_it =Δu_i+c_i(x,t)u_i+1^p_i, (x,t)∈ Ω × (0,∞). 给出了方程组解的整体存在与爆破准则. 这些结果表明, 权重函数c_i(x,t), ψ_i(x,y,t) 和指数 p_i, l_i的大小在确定方程组的解是否爆破中起着关键的作用.

关键词: 抛物型方程组, 非局部边界条件, 权重函数, 整体解, 爆破

Abstract:

This paper considers a semilinear parabolic system u_it =Δu_i+c_i(x,t)u_i+1^p_i for (x,t)∈ Ω × (0,∞) subject to weighted nonlocal Dirichlet boundary conditions ∫_Ωψ_i(x,y,t)u_i^l_i (y,t)dy and nonnegative initial data. Some criteria on this problem which determine whether the solutions blow up in a finite time or the solutions exist for all time are given. These results show that the weight functions c_i(x,t), ψ_i(x,y,t) and the size of exponents p_i, l_i play substantial roles in determining whether the solutions are global or blow-up.

Key words: Parabolic system, Nonlocal boundary condition, Weight function, Global solution, Blow-up

中图分类号:

O175.2

凌征球, 覃思乾. 非线性非局部边界条件的半线性耦合抛物型方程组[J]. 数学物理学报, 2015, 35(2): 234-244.

Ling Zhengqiu, Qin Siqian. Coupled Semilinear Parabolic System with Nonlinear Nonlocal Boundary Condition[J]. Acta mathematica scientia,Series A, 2015, 35(2): 234-244.

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