A study of blow-ups in the Keller–Segel model of chemotaxis
نویسندگان
چکیده
We study the Keller–Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to resolve and propagate singular solutions. We compare the numerical findings (in two dimensions) with analytical predictions regarding formation and interaction of singularities obtained through analysis of the stochastic differential equations associated with the model. PACS numbers: 02.60.Nm, 02.70.Ns, 05.10.Gg, 87.10.Ed, 87.10.Mn, 87.17.Jj Mathematics Subject Classification: 35K58, 45G05, 65C35, 82C22, 82C31, 82C80, 92C17
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