Stability Results for a Diffusion Equation with Functional Drift Approximating a Chemotaxis Model1
نویسنده
چکیده
A hyperbolic-parabolic "chemotaxis" system modelling aggregation of motile cells by production of a diffusible chemoattractant, is approximated by a scalar diffusion equation for the cell density, where the drift term is an explicit functional of the current density profile. We prove the unique existence and, using the Hopf-Cole transformation, the local stability of an equilibrium, i.e. a steady aggregation state. We also discuss the limiting hyperbolic case of vanishing random motility with the formation of shocks describing cell clumps.
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