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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Motivated by the Keller-Segel system of several interacting populations, we studied the existence/non- existence of steady states in the self-similar variables, when the system has an additional drift for each component decaying in time at the rate O$$(1/\sqrt{t})$$ Such steady states satisfy a modified Liouville’s system with a quadratic potential. In this presentation, we will discuss the conditions for existence/non- existence of solutions of such Liouville’s systems, which, in turn, is related to the existence/non-existence of minimizers to a corresponding free energy functional (also called the Lyapunov functional) of the system. This a joint work with Prof. Gershon Wolansky (arXiv:1802.08975).