SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE

doi:10.1016/S0252-9602(15)30092-8

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 244-256.doi: 10.1016/S0252-9602(15)30092-8

SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE

郑攀¹, 穆春来², 胡学刚³, 张付臣⁴

1. Department of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
3. Department of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
4. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

收稿日期:2014-09-15 修回日期:2014-11-20 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Pan ZHENG,E-mail:zhengpan@cqupt.edu.cn;Chunlai MU,E-mail:clmu2005@163.com;Xuegang HU,E-mail:huxg@cqupt.edu.cn;Fuchen ZHANG,E-mail:zhangfuchen1983@163.com
基金资助:
The first author was partially supported by the Doctor Start-up Funding and Natural Science Foundation of Chongqing University of Posts and Telecommunications(A2014-25 and A2014-106); partially supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1500403) and the Basic and Advanced Research Project of CQCSTC(cstc2015jcyjA00008); the second author was partially supported by NSFC(11371384); the fourth author was partially supported by NSFC(11426047), the Basic and Advanced Research Project of CQCSTC(cstc2014jcyjA00040) and the Research Fund of Chongqing Technology and Business University(2014-56-11).

SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE

Pan ZHENG¹, Chunlai MU², Xuegang HU³, Fuchen ZHANG⁴

1. Department of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;
3. Department of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
4. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

Received:2014-09-15 Revised:2014-11-20 Online:2016-01-30 Published:2016-01-30
Supported by:
The first author was partially supported by the Doctor Start-up Funding and Natural Science Foundation of Chongqing University of Posts and Telecommunications(A2014-25 and A2014-106); partially supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1500403) and the Basic and Advanced Research Project of CQCSTC(cstc2015jcyjA00008); the second author was partially supported by NSFC(11371384); the fourth author was partially supported by NSFC(11426047), the Basic and Advanced Research Project of CQCSTC(cstc2014jcyjA00040) and the Research Fund of Chongqing Technology and Business University(2014-56-11).

摘要/Abstract

摘要：

This paper deals with the Cauchy problem for a doubly singular parabolic equa-tion with a weighted source u^t=div(|∇u|^p-2∇u^m)+|x|^αu^q,(x, t)∈R^N×(0, T), where N≥1, 1< p< 2, m>max{0, 3-p-p/N} satisfying 2< p+m< 3, q>1, and α>N(3-p-m)-p.We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem.Moreover, the life span of solutions is also studied.

关键词: life span, secondary critical exponent, doubly singular parabolic equation, weighted source, blow-up

Abstract:

Key words: life span, secondary critical exponent, doubly singular parabolic equation, weighted source, blow-up

中图分类号:

35K55

郑攀, 穆春来, 胡学刚, 张付臣. SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE[J]. 数学物理学报(英文版), 2016, 36(1): 244-256.

Pan ZHENG, Chunlai MU, Xuegang HU, Fuchen ZHANG. SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE[J]. Acta mathematica scientia,Series B, 2016, 36(1): 244-256.

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SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE

SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE

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