Blow up for the solutions of the pressureless Euler-Poisson equations
with time-dependent damping
Abstract
The Euler-Poisson equations can be used to describe the important
physical phenomena in many areas, such as semiconductor modeling and
plasma physics. In this paper, we show the singularity formation
mechanism for the solutions of the pressureless Euler-Poisson equations
with time-dependent damping for the attractive forces in R^n (n ≧1)
and the repulsive forces in R. We obtain the blow up of the derivative
of the velocity under the appropriate assumptions.