On asymptotic behavior and interface curve of solution for Keller-Segel system of degenerate type

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Measure valued solution : The time global solution has been constructed for Keller-Segel system of semi-linear type by expanding the functional space to the measure valued solution.Asymptotics : We have proved that the solution of Keller-Segel system behaves like a stationary solution asymptotically as time tends to infinity.Uniqueness : We have established the functional space which the weak solution becomes unique.Finite speed propagation : The existence of solution and the extinction phenomena has been proved for Keller-Segel system of singular type.