带时滞的退化半线性抛物方程的熄灭(英文) 被引量：1

Quenching for Degenerate Semilinear Parabolic Equations with Time Delay

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摘要考虑带时滞的退化半线性抛物方程的熄灭问题.利用正则化方法和上下解技巧,我们得到了上述问题经典解的存在惟一性,同时还证明了存在一个临界长度a*使得上述问题的解u当a<a*时整体存在,而当a>a*时在有限时间内熄灭.进而我们还得到关于临界长度a*的一个简单估计. This paper deals with the quenching problem for degenerate semilinear parabolic equations with time delay. By using regularization method and upper and lower solutions＇technique, we obtain the existence of a unique classical solution to the above problem and prove that there exists a critical length α ＊ such that the solution u of the above problem exists globally for α 〈 α ＊ and quenches in finite time for α 〉 α ＊. Furthermore, we also get a simple estimate on the critical length α ＊.

作者陈友朋

机构地区盐城师范学院数学系

出处《南京师大学报（自然科学版）》 CAS CSCD 北大核心 2006年第1期7-13,共7页 Journal of Nanjing Normal University(Natural Science Edition)

基金 Supported Partially by the Research Program of the Natural Science of the Universities in Jiangsu Province(05KJB110144).

关键词熄灭问题退化半线性抛物方程时滞临界长度简单估计 quenching problem, degenerate semilinear parabolic equation, time delay, critical length, a simple estimate

分类号 O175.26 [理学—基础数学]

作者简介 Biography： Chen Youpeng, born in 1966, doctor, associate professor, majored in nonlinear partial differential equations.E-mail： youpengc@ yahoo, com. cn

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参考文献1

1陈友朋,谢春红.一带时滞的退化奇异抛物型方程的熄灭[J].南京大学学报（数学半年刊）,2003,20(2):139-150. 被引量：1

二级参考文献20

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同被引文献14

1Pao C V. Nonlinear Parabolic and Elliptic Equations [M] . New York: Plenum Press, 1992.
2Pao C V. Blowing-up of solution for a nonlocal reaction-diffusion problem in combustion theory[J] . Journal of Mathematical and Applications, 1992, 166 (2): 591-600.
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引证文献1

1陆求赐,江秋香.一类带时滞的退化半线性抛物方程组解的存在性研究[J].长江大学学报（自科版）（上旬）,2014,11(10):9-12. 被引量：2

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1陆求赐,王学彬.一类带时滞的Lotka-Volterra竞争扩散模型周期解的收敛性质研究[J].赤峰学院学报（自然科学版）,2018,34(9):17-19. 被引量：1
2张亮,李建军.一类半线性抛物方程的解的爆破性质研究[J].应用数学进展,2017,6(1):10-19. 被引量：1

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3陈友朋,谢春红.一带时滞的退化奇异抛物型方程的熄灭[J].南京大学学报（数学半年刊）,2003,20(2):139-150. 被引量：1
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