The Keller-Segel system on networks (Theory of evolution equations and applications to nonlinear problems)

Abstract

This paper is a review of the results contained in [3] where the well posedness of the Keller-Segel system defined on a weighted network is studied. Completing the system with appropriate transmission conditions at the vertices, we prove global in time existence and uniqueness of a continuous solution of the problem. An important ingredient of the proof is a formula for the Gaussian kernel on networks due to Roth [14] that we briefly recall.