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Numerical study of two-species chemotaxis models. (English) Zbl 1282.92011
Summary: We first conduct a comparative numerical study of two recently proposed two-species chemotaxis models. We show that different scenarios are possible: depending on the initial masses, either one or both cell densities may blow up, or a global solution may exist. In particular, our numerical results indicate answers on some open questions of possible blow up stated by C. Conca et al [Eur. J. Appl. Math. 22, No. 6, 553–580 (2011; Zbl 1241.35025)] and E. Espejo et al. [ibid. 24, No. 2, 297–313 (2013; Zbl 1284.35448)]. We then introduce two regularizations of the studied models and demonstrate that their solutions are capable of developing spiky structures without blowing up.

MSC:
92C17 Cell movement (chemotaxis, etc.)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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