We study the singular limit of a degenerate nonlinear diffusion equation which appears in a chemotaxis-growth model. We prove the convergence to the solution of a free boundary problem where the motion equation of the interface involve the gradient of the chemotactic concentration and the critical velocity of a degenerate Fisher equation.
"Singular limit of a degenerate chemotaxis-Fisher equation." Hiroshima Math. J. 34 (1) 101 - 115, March 2004. https://doi.org/10.32917/hmj/1150998073