Instrability and finite time blow up of solutions to a drift-diffusion system in higher dimensions
主 题: Instrability and finite time blow up of solutions to a drift-diffusion system in higher dimensions
报告人: Professor Takayoshi Ogawa (Tohoku University)
时 间: 2017-10-10 15:00-16:00
地 点: 理科1号楼1303
Abstract: We consider a large time behavior of solutions to drift-diffusion systems in higher dimensions. The drif-diffusion system is derived from a fluid mechanical approximation and it describe a typical behavior of more complicated system such as compressible-Naveir-Stokes-Poisson equations. The equation has a diffusive exponent and it classify the nature of the solution.
We consider both the semilinear and quasilinear cases and show that solutions of both cases are unstable under certain conditions on the data and that the solution grows to infinity as time goes infinity. For a radially symmetric case, the solution blows up in a finite time and the mass concentration phenomena occurs when the exponent is the mass critical case.