This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β...This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β,γwith 0<■,which has been studied under the initial condition Jp(u0)<0.This paper generalizes the above results on the following aspects:a new blow-up condition is given,which holds for all p>2;a new blow-up condition is given,which holds for p=2;some new lifespans and upper blow-up rates are given under certain conditions.展开更多
We investigate the initial boundary value problem of the pseudo-parabolic equation ut-/△ut-/△u=φuu+|u|p-1u,whereφu is the Newtonian potential,which was studied by Zhu et al.(Appl.Math.Comput.,329(2018)38-51),and t...We investigate the initial boundary value problem of the pseudo-parabolic equation ut-/△ut-/△u=φuu+|u|p-1u,whereφu is the Newtonian potential,which was studied by Zhu et al.(Appl.Math.Comput.,329(2018)38-51),and the global existence and the finite time blow-up of the solutions were studied by the potential well method under the subcritical and critical initial energy levels.We in this note determine the upper and lower bounds for the blow-up time.While estimating the upper bound of blow-up time,we also find a sufficient condition of the solution blowingup in finite time at arbitrary initial energy level.Moreover,we also refine the upper bounds for the blow-up time under the negative initial energy.展开更多
基金Supported by the Doctoral Scientific Research Starting Foundation of Guizhou Normal University of China,2018(No.GZNUD[2018]34 and 11904/0519113).
文摘This article investigates the blow-up results for the initial boundary value problem to the quasi-linear parabolic equation with p-Laplacian■where p≥2 and the function f(u)satisfies■for some positive constantsα,β,γwith 0<■,which has been studied under the initial condition Jp(u0)<0.This paper generalizes the above results on the following aspects:a new blow-up condition is given,which holds for all p>2;a new blow-up condition is given,which holds for p=2;some new lifespans and upper blow-up rates are given under certain conditions.
基金Supported by the Doctoral Scientific Research Starting Foundation of Guizhou Normal University of China,2018(No.GZNUD[2018]34).
文摘We investigate the initial boundary value problem of the pseudo-parabolic equation ut-/△ut-/△u=φuu+|u|p-1u,whereφu is the Newtonian potential,which was studied by Zhu et al.(Appl.Math.Comput.,329(2018)38-51),and the global existence and the finite time blow-up of the solutions were studied by the potential well method under the subcritical and critical initial energy levels.We in this note determine the upper and lower bounds for the blow-up time.While estimating the upper bound of blow-up time,we also find a sufficient condition of the solution blowingup in finite time at arbitrary initial energy level.Moreover,we also refine the upper bounds for the blow-up time under the negative initial energy.
