一类双重退化抛物型不等式问题解的Liouville 型定理

数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 639-643.

一类双重退化抛物型不等式问题解的Liouville 型定理

姜朝欣, 郑斯宁

大连理工大学数学科学学院大连 116024

收稿日期:2008-11-25 修回日期:2009-10-13 出版日期:2010-05-25 发布日期:2010-05-25
基金资助:
国家自然科学基金(10771024)资助

A Liouville-type Theorem for a Doubly Degenerate Parabolic Inequality

JIANG Chao-Xin, ZHENG Si-Ning

School of Mathematical Sciences, Dalian University of Technology, Dalian 116024

Received:2008-11-25 Revised:2009-10-13 Online:2010-05-25 Published:2010-05-25
Supported by:
国家自然科学基金(10771024)资助

摘要/Abstract

摘要：

该文对一类双重退化抛物型不等式问题建立了弱解的Liouville 型定理. 不同于通常的上下解方法, 这里采用更为简洁的适当选取试验函数与能量估计的方法证明整体解的不存在性.

关键词: Fujita 临界指标, Liouville 型定理, 双重退化, 抛物型不等式, blow-up

Abstract:

This paper deals with the nonexistence of nontrivial nonnegative global solutions to a doubly degenerate parabolic inequality u_t ≥ div(|\nabla
u| ^β\nabla u ^m)+u ^p on the half space S=Rⁿ×(0, ∞), where the parameters m≥1, p>1, β≥0. By using a test function method, we establish a Liouville-type theorem tha the inequality has no nontrivial nonnegative solution on S if m+β< p <m+β+β+2/n.

Key words: Critical Fujita exponent, Liouville-type theorem, Doubly degenerate, Parabolic inequality, blow-up

中图分类号:

35B33

姜朝欣, 郑斯宁. 一类双重退化抛物型不等式问题解的Liouville 型定理[J]. 数学物理学报, 2010, 30(3): 639-643.

JIANG Chao-Xin, ZHENG Si-Ning. A Liouville-type Theorem for a Doubly Degenerate Parabolic Inequality[J]. Acta mathematica scientia,Series A, 2010, 30(3): 639-643.

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