Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation

In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial energy are established. Then these results are extended parallelly to the critical initial energy. Further the blowup phenomena of solution with supercritical initial energy is proved, but the existence, uniqueness and asymptotic behavior of the global solution with supercritical initial energy are still open.