Blow-up phenomena for some nonlinear pseudo-parabolic equations

This paper considers the blow-up of solutions for equations ut−ν△ut=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).