Note on blow up solutions for a general class of semilinear parabolic equations involving second order operator

Source abstract

This work deals with an initial-boundary value problem of Laplacian parabolic equation ( h ( u ) ) t + △ p u = f ( u ( x , t ) ) , in Ω × ( 0 , ∞ ) , u ( x , t ) = 0 , on ∂ Ω × ( 0 , ∞ ) , u ( x 0 ) = u 0 ≥ 0 , x ∈ Ω ¯ , where Ω is a bounded domain in R N , N ≥ 1 . Our contribution is to give a new condition on nonlinearity to obtain the blow-up solutions of the above equations.