Abstract. In this paper, we are interested in the numerical simulation of the mathematical model of Keller-Segel Elliptic-Parabolic problem using finite volume scheme. The finite volume scheme is applied to the elliptic-parabolic model's problem and we have shown under certain assumptions, the existence of a unique and positive approximate solution. Moreover, under adequate regularity assumption of the exact solution, the finite volume scheme is the first order accurate. A good agreement between our numerical simulation and the theoretical results has been obtained.

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Oscillatory behavior of solutions of coupled hyperbolic partial differential equations is justified and generalized for a large class of problems. To achieve our goal, we use some techniques based essentially on some tools related to ordinary differential inequalities theory.