一类双重退化抛物方程组解的整体存在与爆破

宋小军, 米永生, 穆春来

数学学报 ›› 2012 ›› Issue (2) : 281-292.

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PDF(548 KB)
数学学报 ›› 2012 ›› Issue (2) : 281-292. DOI: 10.12386/A2012sxxb0028
论文

一类双重退化抛物方程组解的整体存在与爆破

    宋小军1, 米永生2, 穆春来3
作者信息 +

Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic Equations

    Xiao Jun SONG1, Yong Sheng MI2, Chun Lai MU3
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摘要

研究一类具有非线性边界流的双重退化抛物方程组解的整体存在与爆破,通过构造自相似的上下解,得到了整体存在曲线.借助一些新的结果,获得了Fujita临界指数.其中一个有趣的现象是:整体存在曲线和Fujita临界曲线分别是由一个矩阵和线性方程组来决定.

Abstract

The paper deals with the critical curve for a degenerate parabolic system coupled via nonlinear boundary flux. By constructing the self-similar super-solution and sub-solution, we obtain the critical global existence curve. And the critical curve of Fujita type is conjectured with the aid of some new results. An interesting feature of our results is that the critical global existence curve and the critical Fujita curve are determined by a matrix and by the solution of a linear algebraic system, respectively.

关键词

整体存在指数 / Fujita临界指数 / 爆破

Key words

critical global existence curve / critical Fujita curve / blow-up

引用本文

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宋小军, 米永生, 穆春来. 一类双重退化抛物方程组解的整体存在与爆破. 数学学报, 2012(2): 281-292 https://doi.org/10.12386/A2012sxxb0028
Xiao Jun SONG, Yong Sheng MI, Chun Lai MU. Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic Equations. Acta Mathematica Sinica, Chinese Series, 2012(2): 281-292 https://doi.org/10.12386/A2012sxxb0028

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基金

国家自然科学基金资助项目(11071266);重庆市自然科学基金资助项目(2010BB9218)

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