Blow-up phenomena for some nonlinear pseudo-parabolic equations

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

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