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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 \begin{document}$L^2$\end{document} -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.

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