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Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. (English) Zbl 1065.92006
Summary: We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by E. F. Keller and L. A. Segel [J. Theor. Biol. 30, 225–234 (1971)]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of PDE. is approximated via a mixed finite element technique. The solution algorithm is then described and finally we give some preliminary numerical results. Especially our method is well adapted to compute the concentration of bacteria.

MSC:
92C17 Cell movement (chemotaxis, etc.)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
92C40 Biochemistry, molecular biology
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