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Efendiyev, M.A. ; Zhigun, A.

On a 'balance' condition for a class of PDEs including porous medium and chemotaxis effect: Non-aoutonomous case.

Adv. Math. Sci. Appl. 21, 285-304 (2011)

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In this article we deal with a class of degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We prove well-posedness under certain ”balance conditions” on the order of the porous medium degeneracy and the growth of the chemotactic functions.

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