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

Yoshifumi Mimura | Zendy

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

Author(s) -

Yoshifumi Mimura

Publication year - 2016

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2017066

Subject(s) - degenerate energy levels , boundary (topology) , space (punctuation) , critical mass (sociodynamics) , neumann boundary condition , mathematics , variable (mathematics) , flow (mathematics) , mathematical analysis , mass flux , constant (computer programming) , scheme (mathematics) , von neumann architecture , balanced flow , physics , pure mathematics , geometry , computer science , mechanics , quantum mechanics , social science , sociology , programming language , operating system

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.

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