Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux

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• 作者：Zhong Bo Fang ; Yuxiang Wang
• 关键词：35K65 ; 35B30 ; 35B40 ; Semilinear parabolic equation ; Time ; dependent coefficients ; Blow ; up time ; Upper bound ; Lower bound
• 刊名：Zeitschrift f篓鹿r angewandte Mathematik und Physik
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：66
• 期：5
• 页码：2525-2541
• 全文大小：552 KB
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• 作者单位：Zhong Bo Fang (1)
  Yuxiang Wang (1)
  
  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, People鈥檚 Republic of China
  
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer Basel
• ISSN：1420-9039

文摘

A blow-up analysis for a nonlinear divergence form of parabolic equation with time-dependent coefficients is given under nonlinear boundary flux in a bounded star-shaped region. We establish some conditions on time-dependent coefficients and nonlinearities to guarantee existence of global solution or blow-up solution at some finite time t*. Moreover, an upper bound for t* is derived. Under somewhat more restrictive conditions, a lower bound for t* can be obtained. Finally, some application examples to verify the bounds of t* are presented. Keywords Semilinear parabolic equation Time-dependent coefficients Blow-up time Upper bound Lower bound