Blow-up of porous medium equations with variable source power

2016 ◽  
Vol 46 (3) ◽  
pp. 265-284
Author(s):  
ShuLin ZHOU ◽  
YuanCheng XIE ◽  
Zhi ZHENG
Keyword(s):  
Porous Medium ◽  
Blow Up ◽  
Source Power ◽  
Variable Source ◽  
Porous Medium Equations

scholarly journals Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source

2020 ◽  
Vol 13 (3) ◽  
pp. 645-662
Author(s):  
Huafei Di ◽  
Lin Chen ◽  
Zefang Song
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Lower Bounds ◽  
Blow Up ◽  
Neumann Boundary ◽  
Upper Bounds ◽  
Neumann Boundary Conditions ◽  
Integral Inequalities ◽  
Porous Medium Equations ◽  
Blow Up Rate

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.

Blow-up of p-Laplacian evolution equations with variable source power

2016 ◽  
Vol 60 (3) ◽  
pp. 469-490 ◽  
Author(s):  
Zhi Zheng ◽  
YuanWei Qi ◽  
ShuLin Zhou
Keyword(s):  
Evolution Equations ◽  
Blow Up ◽  
Source Power ◽  
Variable Source
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