Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source
Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source
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DOI：
10.29020/nybg.ejpam.v13i3.3768
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发表时间：
2020-07
影响因子：
0.7
通讯作者：
Huafei Di;Lin Chen;Zefang Song
中科院分区：
文献类型：
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作者：
Huafei Di;Lin Chen;Zefang Song
研究一类带权源的非线性多孔介质方程ut −4um = a（x）f（u）在Dirichlet（或Neumann）边界条件下的爆破现象.基于辅助函数和微分积分不等式，在两种不同的假设下，给出了u不可能始终存在的爆破准则，并分别得到了相应的爆破时间和爆破速率的上界估计.此外，我们使用三种不同的方法来确定爆破时间和爆破率估计的下界，如果爆破确实发生。
This paper deals with the blow-up phenomena for a type of nonlinear porous medium equations with weighted source ut −4um = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions. Based on the auxiliary functions and differential-integral inequalities, the blow-up criterions which ensure that u cannot exist all time are given under two different assumptions, and the corresponding estimates on the upper bounds for blow-up time and blow-up rate are derived respectively. Moreover, we use three different methods to determine the lower bounds for blow-up time and blow-up rate estimates if blow-up does occurs.