@article{adeb753d15c44aa0a36279b83e17282b,
title = "Stability and instability of solutions to the drift-diffusion system",
abstract = "We consider the large time behavior of a solution to a drift-diffusion equation for degenerate and non-degenerate type. We show an instability and uniform unbounded estimate for the semi-linear case and uniform bound and convergence to the stationary solution for the case of mass critical degenerate case for higher space of dimension bigger than two.",
keywords = "Boundedness, Drift diffusion system, Finite time blow up, Scaling critical, Stability",
author = "Takayoshi Ogawa and Hiroshi Wakui",
note = "Funding Information: 2000 Mathematics Subject Classification. Primary: 35K15, 35K55, 35Q60; Secondary: 78A35. Key words and phrases. Drift diffusion system, stability, boundedness, finite time blow up, scaling critical. The work of T. Ogawa and H. Wakui are partially supported by grant in aid for Scientific Research S #24220702 of JSPS. Publisher Copyright: {\textcopyright} 2017, American Institute of Mathematical Sciences. All rights reserved.",
year = "2017",
month = dec,
doi = "10.3934/eect.2017029",
language = "English",
volume = "6",
pages = "587--597",
journal = "Evolution Equations and Control Theory",
issn = "2163-2472",
publisher = "American Institute of Mathematical Sciences",
number = "4",
}