Anomalous Pseudo-Parabolic Kirchhoff-Type Dynamical Model

In this paper, we study an anomalous pseudo-parabolic Kirchhoff-type dynamical model aiming to reveal the control problem of the initial data on the dynamical behavior of the solution in dynamic control system. Firstly, the local existence of solution is obtained by employing the Contraction Mapping Principle. Then, we get the global existence of solution, long time behavior of global solution and blowup solution for J(u(0)) <= d, respectively. In particular, the lower and upper bound estimates of the blowup time are given for J(u(0)) < d. Finally, we discuss the blowup of solution in invinite time and also estimate an upper bound of the blowup time for high initial energy.