| 带有反平方势函数的半线性热方程解的爆破 |
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| 引用本文： | 冯志敏,张岩,穆春来.带有反平方势函数的半线性热方程解的爆破[J].西南师范大学学报(自然科学版),2010,35(2). |
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| 作者姓名： | 冯志敏 张岩 穆春来 |
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| 作者单位： | 1. 重庆大学,数理学院,重庆,400044
2. 西华大学,数学与计算机学院,成都,610039 |
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| 摘 要： | 考虑了半线性热方程ut=Δu-V(x)u+a(x)up在非线性非局部的边界条件u(x,t)=∫ΩK(x,y)ul(y,t)dy下解的性质,通过构造上、下解,得出方程的解整体存在和有限时刻爆破的充分条件.
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| 关 键 词： | 半线性热方程 非局部边界条件 整体存在 爆破 |
Blow-up of Solutions for Semilinear Heat Equation with Inverse-square Potential |
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| FENG Zhi-min,ZHANG Yan,MU Chun-lai.Blow-up of Solutions for Semilinear Heat Equation with Inverse-square Potential[J].Journal of Southwest China Normal University(Natural Science),2010,35(2). |
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| Authors: | FENG Zhi-min ZHANG Yan MU Chun-lai |
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| Abstract: | This paper considers the properties of solutions for a semilinear heat equation u_t=△u-V(x)u+ a(x)u~p for (x,t)∈Ω×(0, ∞) with nonlinear and nonlocal boundary condition u(x, t)=∫_ΩK(x, y)u~∫(y, t)dy on Ω× (0,∞). The conditions on the existence and nonexistence of global solutions are given by utilizing the method of subsolution and supersolution. |
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| Keywords: | semilinear heat equation nonlocal boundary condition global solution blow-up |
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