理论数学  >> Vol. 5 No. 3 (May 2015)

具非局部非线性项的抛物方程的熄灭解
The Quenching Solutions of Parabolic Problems with Reaction Terms of Nonlocal and Nonlinear Type

DOI: 10.12677/PM.2015.53016, PDF, HTML, XML, 下载: 2,006  浏览: 5,128  科研立项经费支持

作者: 郑祥成, 侯全刚, 杨 昊:中国石油大学(华东)理学院,山东 青岛

关键词: 非局部抛物方程熄灭解熄灭速率熄灭集Nonlocal Parabolic Equation Quenching Solution Quenching Rate Quenching Collection

摘要: 本文研究了一类具有非局部非线性项的抛物方程问题解的熄灭性质,在一定对初值的假设条件下,得到了解发生熄灭的判据,进而我们证得了解的熄灭速率和熄灭集合。
Abstract: In this paper, we study quenching problems for solutions of parabolic problems with reaction terms of nonlocal and nonlinear type. Setting some assumptions to the initial data, we acquire the criterion of whether or not the solutions will quench and we prove the quenching rates and quenching collection.

文章引用: 郑祥成, 侯全刚, 杨昊. 具非局部非线性项的抛物方程的熄灭解[J]. 理论数学, 2015, 5(3): 100-104. http://dx.doi.org/10.12677/PM.2015.53016

参考文献

[1] Kawarada, H. (1975) On solutions of initial-boundary problem . Publications of the Research Institute for Mathematical Sciences, 10, 729-736.
[2] Ferreira, R., Pablo, A., Quiros, F., et al. (2006) Non-simultaneous quenching in a system of heat equations coupled at the boundary. Zeitschrift für Angewandte Mathematik und Physik ZAMP, 57, 586-594.
[3] Levine, H.A. (1985) The phenomenon of quenching: A survey. In: Lakshmikantham, V., Ed., Trends in the Theory and Practice of Nonlinear Analysis, Elsevier Science, North Holland, 275-286.
[4] de Pablo, A., Quiros, F. and Rossi, J.D. (2002) Nonsimltaneous quenching. Applied Mathematics Letters, 13, 265-269.
[5] Zhou, J., He, Y. and Mu, C.L. (2008) Imcomplete quenching of heat equations with absorption. Applicable Analysis, 87, 523-529.
[6] 叶其孝, 李正元, 王明新, 吴雅萍 (2013) 反应扩散方程引论. 科学出版社, 北京.