Blow-up phenomena for some nonlinear pseudo-parabolic equations
Blow-up phenomena for some nonlinear pseudo-parabolic equations
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DOI：
10.1016/j.aml.2015.12.005
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
Xiaoming Peng;Y. Shang;Xiaoxiao Zheng
中科院分区：
文献类型：
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作者：
Xiaoming Peng;Y. Shang;Xiaoxiao Zheng
利用微分不等式技巧研究了方程u t−νut=div(ρ(|∇u|2)∇u)+f(U)解的爆破问题.如果确实发生了爆破，则确定爆破时间的下限。在一定条件下，我们建立了爆破准则和爆破的上界。此外，还给出了保证不会发生爆破的条件。这一结果推广了徐荣中(2007)和罗培伦(2015)的结果。
This paper considers the blow-up of solutions for equations u t− ν△ u t= div (ρ (∣∇ u∣ 2)∇ u)+ f (u) by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur. Also, we establish a blow-up criterion and an upper bound for blow-up under some conditions. Moreover, conditions which ensure that blow-up cannot occur are presented. This result extends the results obtained by R. Xu (2007) and P. Luo (2015).