Blow-up and global solutions for a class of nonlinear parabolic equations with different kinds of boundary conditions
Abstract By constructing different auxiliary functions and using Hopf’s maximum principle, the sufficient conditions for the blow-up and global solutions are presented for nonlinear parabolic equation u t  = ∇( a ( u ) b ( x ) c ( t )∇ u ) +  f ( x ,  u ,  q ,  t ) with different kinds of boundary conditions. The upper bounds of the “blow-up time” and the “upper estimates” of global solutions are provided. Finally, some examples are presented as the application of the obtained results.