Evolution Equations and Control Theory (EECT)

Stability and instability of solutions to the drift-diffusion system

Pages: 587 - 597, Volume 6, Issue 4, December 2017      doi:10.3934/eect.2017029

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Takayoshi Ogawa - Tohoku University, Mathematical Institute, Sendai 980-8578, Japan (email)
Hiroshi Wakui - Mathematical Institute, Tohoku University, Sendai 980-8578, Japan (email)

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:  Drift diffusion system, stability, boundedness, finite time blow up, scaling critical.
Mathematics Subject Classification:  Primary: 35K15, 35K55, 35Q60; Secondary: 78A35.

Received: March 2017;      Revised: August 2017;      Available Online: September 2017.