Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source - Di, Huafei; Chen, Lin; Song, Zefang (European journal of pure and applied mathematics, 2020)
This paper deals with the blow-up phenomena for a type of nonlinear porous medium equations with weighted source ut âˆ’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.