Unboundedness for solutions to a degenerate drift-diffusion equation under non-weight condition

Speaker(s)

Hiroshi Wakui

Affiliation

Tohoku University/ Uniwersytet Wrocławski

Date

March 28, 2019, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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In this talk, we consider unboundedness and concentration phenomenon of solutions to a degenerate drift-diffusion equation. We proved that solutions do not remain bounded in time when the initial data has negative free energy under a non-weight condition with the mass critical case. Moreover, we show that the mass concentration phenomenon of radially symmetric solutions to our problem occurs with the sharp lower bound related to the best constant of the Hardy-Littlewood-Sobolev inequality. Moreover, an estimate of the concentration rate of the total mass is given by the natural rate which is induced by the natural invariant scaling of our problem. We note that the sharp lower bound can be estimated by the well-known value 8π when we take the limit with respect to the dimension to 2.

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