Anomalous pseudo-parabolic Kirchhoff-type dynamical model

Abstract

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 finite time and also estimate an upper bound of the blowup time for high initial energy.

The high-order smooth interpolated reproducing kernel particle method for elastodynamics problems

“…Without the dependence of the grids, the output displacement, strain, and stress are continuous in the whole analysis domain, and the error of the quadratic approximation is avoided [29,30]. Two mainstream meshless methods are the element-free Galerkin methods [31][32][33][34][35] and the reproducing kernel particle methods [36][37][38][39]. However, the meshless method based on the Galerkin discretization scheme is not easy to apply the boundary conditions.…”