Stability and instability of solutions to the drift-diffusion system

Takayoshi Ogawa; Hiroshi Wakui

doi:10.3934/eect.2017029

Article Contents

2017, Volume 6, Issue 4: 587-597. Doi: 10.3934/eect.2017029

This issue Previous Article Some problems of guaranteed control of the Schlögl and FitzHugh-Nagumo systems Next Article Exact controllability results for a class of abstract nonlocal Cauchy problem with impulsive conditions

Stability and instability of solutions to the drift-diffusion system

Takayoshi Ogawa^1, and
Hiroshi Wakui^2,

1.
Tohoku University, Mathematical Institute, Sendai 980-8578, Japan
2.
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan

Received: February 28, 2017

Revised: July 31, 2017

Published: November 2017

The work of T. Ogawa and H. Wakui are partially supported by grant in aid for Scientific Research S #24220702 of JSPS.

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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.

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Mathematics Subject Classification: Primary: 35K15, 35K55, 35Q60; Secondary: 78A35.

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References

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