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Stability and instability of solutions to the drift-diffusion system

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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  • 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.

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

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