THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (4): 413-420.

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

林支桂¹, 谢春红¹, 王明新²

1. Department of Mathematics, Nanjing University, Nanjing 210093, China;
2. Department of mathematics and mechanics, Southeast University, Nanjing 210018, China

收稿日期:1996-12-10 修回日期:1997-03-10 出版日期:1998-12-25 发布日期:1998-12-25
基金资助:
This auther's work was supported by the National Naturcd Scdence Foundation of China.

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

Lin Zhigui¹, Xie Chunhong¹, Wang Mingxin²

1. Department of Mathematics, Nanjing University, Nanjing 210093, China;
2. Department of mathematics and mechanics, Southeast University, Nanjing 210018, China

Received:1996-12-10 Revised:1997-03-10 Online:1998-12-25 Published:1998-12-25
Supported by:
This auther's work was supported by the National Naturcd Scdence Foundation of China.

摘要/Abstract

摘要： This paper deals with the blow-up properties of solutions to the systems u_t △u=e^v(x₀,t), v_t-△v=e^v(x₀,t) in Ω×(0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.

关键词: parabolic system, blow-up rate, blow-up set

Abstract: This paper deals with the blow-up properties of solutions to the systems u_t △u=e^v(x₀,t), v_t-△v=e^v(x₀,t) in Ω×(0,T) subject to either initial conditions or the initial and boundary-value conditions. The authors show that under certain conditions the solution blows up in finite time and prove that the set of all blow-up points is the whole region. Moreover, the exact blow-up rates are also derived.

Key words: parabolic system, blow-up rate, blow-up set

林支桂, 谢春红, 王明新. THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS[J]. 数学物理学报(英文版), 1998, 18(4): 413-420.

Lin Zhigui, Xie Chunhong, Wang Mingxin. THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS[J]. Acta mathematica scientia,Series B, 1998, 18(4): 413-420.

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THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

THE BLOW-UP PROPERTIES OF SOLUTIONS TO A PARABOLIC SYSTEM WITH LOCALIZED NONLINEAR REACTIONS

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