Global blow-up for a localized nonlinear parabolic equation with a nonlocal boundary condition

This paper deals with the blow-up properties of positive solutions to a nonlinear parabolic equation with a localized reaction source and a nonlocal boundary condition. Under certain conditions, the blowup criteria is established. Furthermore, when f(u)=up, 0<p?1, the global blowup behavior is shown, and the blowup rate estimates are also obtained.     

The Nonlinear Schr(o)dinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type

The primary goal of this paper is to present a comprehensive study of the nonlinear Schr(o)dinger equations with combined nonlinearities of the power-type and Hartreetype. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schr(o)dinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles.     

Moving collocation methods for time fractional differential equations and simulation of blowup

A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.