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Critical mass of degenerate Keller-Segel system with no-flux and Neumann boundary conditions

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  • We prove the existence of solutions of degenerate parabolic-parabolic Keller-Segel system with no-flux and Neumann boundary conditions for each variable respectively, under the assumption that the total mass of the first variable is below a certain constant. The proof relies on the interpretation of the system as a gradient flow in the product space of the Wasserstein space and the standard $L^2$-space. More precisely, we apply the ''minimizing movement'' scheme and show a certain critical mass appears in the application of this scheme to our problem.

    Mathematics Subject Classification: 35K65, 35B33, 47J30, 35K40.


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