一个具有耦合边界流的热方程组的爆破估计的注解

李中平, 穆春来

数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 197-202.

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PDF(348 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (2) : 197-202. DOI: 10.12386/A2013sxxb0020
论文

一个具有耦合边界流的热方程组的爆破估计的注解

    李中平1, 穆春来2
作者信息 +

A Note on Blow-up Estimates for a System of Heat Equations Coupled Boundary Flux

    Zhong Ping LI1, Chun Lai MU2
Author information +
文章历史 +

摘要

在本注解中,我们采用Scaling方法,得到了具有耦合边界流的热方程组的爆破估计.

Abstract

In this note, we adapt the scaling method and give the blow-up estimates for a system of heat equations coupled boundary flux.

关键词

爆破估计 / 热方程 / 非线性边界流

Key words

blow-up estimates / heat equations / nonlinear boundary flux

引用本文

导出引用
李中平, 穆春来. 一个具有耦合边界流的热方程组的爆破估计的注解. 数学学报, 2013, 56(2): 197-202 https://doi.org/10.12386/A2013sxxb0020
Zhong Ping LI, Chun Lai MU. A Note on Blow-up Estimates for a System of Heat Equations Coupled Boundary Flux. Acta Mathematica Sinica, Chinese Series, 2013, 56(2): 197-202 https://doi.org/10.12386/A2013sxxb0020

参考文献

[1] Fan M. S., Du L. L., Simultaneous versus nonsimultaneous blowup for a system of heat equations coupled boundary flux, Boundary Value Problems, 2007, 2007: Article ID 75258.

[2] Zhao L. Z., Zheng S. N., Blow-up estimates for system of heat equations coupled via nonlinear boundary flux, Nonlinear Anal., 2003, 54: 251-259.

[3] Hu B., Yin H. M., The profile near blowup time for solution of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 1994, 346: 117-135.

[4] Quirós F., Rossi J. D., Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions, Indiana Univ. Math. J., 2001, 50: 629-654.

[5] Friedman A., Partial Differential Equations of Parabolic Type, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1964.

[6] Lieberman G. M., Second Order Parabolic Differential Equations, World Scientific, River Edge, NJ, 1996.

基金

国家自然科学基金资助项目(11071266);国家自然科学数学天元基金项目(11226181);西华师范大学校启动科院项目(12B024)

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