非局部退化拟线性抛物型方程组解的爆破和整体存在性

数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 386-396.

非局部退化拟线性抛物型方程组解的爆破和整体存在性

陈玉娟

东南大学数学系|南京210097|南通大学理学院|江苏南通 |226007

收稿日期:2008-03-25 修回日期:2009-01-12 出版日期:2010-04-25 发布日期:2010-04-25
基金资助:
国家自然科学基金(10671210)、江苏省教育厅自然科学指导性计划项目 (07KJD110166)、江苏省青蓝工程以及
南通大学立项资助项目(06Z011, 08B02)资助.

Blow-up and Global Existence for |a Nonlocal Degenerate Quasilinear Parabolic System

CHEN Yu-Juan

Department of Mathematics, Southwest University, Nanjing 210097|School of |Science, Nantong University, Jiangsu Nantong 226007

Received:2008-03-25 Revised:2009-01-12 Online:2010-04-25 Published:2010-04-25
Supported by:
国家自然科学基金(10671210)、江苏省教育厅自然科学指导性计划项目 (07KJD110166)、江苏省青蓝工程以及
南通大学立项资助项目(06Z011, 08B02)资助.

摘要/Abstract

摘要：

该文采用弱上下解方法和正则化技巧,研究了一类非局部退化抛物型方程组解的爆破和整体存在性,给出了爆破指标, 并对非退化情形m = n = 1, p₁ = q₁=0, p₂q₂>1给出了一致爆破速率.

关键词: 退化抛物型方程组, 非局部源;爆破, 整体存在性

Abstract:

This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal
degenerate parabolic system. The sub-and-super solutions method and the regularization skill are used. The critical exponent of the system is gained. Furthermore, for the special case m = n = 1, p₁= q₁=0, p₂q₂>1, the uniform blow-up profile is gained.

Key words: Degenerate parabolic system, Nonlocal source, Global existence, Blow-up

中图分类号:

35K55

陈玉娟. 非局部退化拟线性抛物型方程组解的爆破和整体存在性[J]. 数学物理学报, 2010, 30(2): 386-396.

CHEN Yu-Juan. Blow-up and Global Existence for |a Nonlocal Degenerate Quasilinear Parabolic System[J]. Acta mathematica scientia,Series A, 2010, 30(2): 386-396.

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