一类具有局部化源和吸收项的抛物系统解的整体存在与爆破

周军

数学学报 ›› 2013, Vol. 56 ›› Issue (1) : 67-86.

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数学学报 ›› 2013, Vol. 56 ›› Issue (1) : 67-86. DOI: 10.12386/A2013sxxb0008
论文

一类具有局部化源和吸收项的抛物系统解的整体存在与爆破

    周军
作者信息 +

Global Existence and Blow-up Properties for a Parabolic System with Localized Source and Absorption

    Jun ZHOU
Author information +
文章历史 +

摘要

在齐次Dirichlet边界条件研究如下抛物系统
其中x0(t):R+→(0,a)是Hölder连续函数; 常数0≤α,β<1, p1,p2,q1,q2,k1,k2>0. 利用正则化方法,在一定的假设条件下证明了经典解的存在性. 接着利用比较原理证明了该系统正解的整体存在性和爆破性. 最后给出了爆破解的精确爆破速率和爆破模式.

Abstract

The aim of this paper is to investigate the following parabolic system

under homogeneous Dirichlet boundary condition, where x0(t):R+→(0,a) is Hölder continuous, and the constants 0≤α, β <1, p1,p2,q1,q2,k1,k2>0. Under appropriate hypotheses, we first prove the local existence of classical solution by a regularization method. Then we discuss the global existence and blow-up of positive solutions by using a comparison principle. Finally, we give the precise blow-up estimates and the uniform blow-up profiles.

关键词

退化奇异抛物系统 / 整体存在 / 爆破速率 / 爆破模式

Key words

degenerate and singular parabolic system / global existence / blow-up rate / uniform blow-up profiles

引用本文

导出引用
周军. 一类具有局部化源和吸收项的抛物系统解的整体存在与爆破. 数学学报, 2013, 56(1): 67-86 https://doi.org/10.12386/A2013sxxb0008
Jun ZHOU. Global Existence and Blow-up Properties for a Parabolic System with Localized Source and Absorption. Acta Mathematica Sinica, Chinese Series, 2013, 56(1): 67-86 https://doi.org/10.12386/A2013sxxb0008

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基金

国家自然科学数学天元基金(11126141);国家自然科学青年基金(11201380);中央高校基本科研业务费重点项目(XDJK2012B007);西南大学博士基金(SWU111021)及教育基金(2010JY053)

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