Bounds for blow-up time in a semilinear pseudo-parabolic equation with nonlocal source - Yang Lu; Liang Fei (Journal of Inequalities and Applications, 2016)
Abstract This paper considers the following semilinear pseudo-parabolic equation with a nonlocal source: u t − △ u t − △ u = u p ( x , t ) ∫ Ω k ( x , y ) u p + 1 ( y , t ) d y , $$ u_{t}-\triangle u_{t}-\triangle u=u^{p}(x,t) \int_{Ω}k(x,y)u^{p+1}(y,t)\,dy, $$ and it explores the characters of blow-up time for solutions, obtaining a lower bound as well as an upper bound for the blow-up time under different conditions, respectively. Also, we investigate a nonblow-up criterion and compute an exact exponential decay.