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Blow-up behavior of solutions to a parabolic-elliptic system on higher dimensional domains

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  • We consider a parabolic-elliptic system of equations that arises in modelling the chemotaxis in bacteria and the evolution of self-attracting clusters. In the case space dimension $3 \leq N \leq 9$, we will derive criteria of the blow-up rate of solutions, and identify an explicit class of initial data for which the blow-up is of self-similar rate. Our argument is based on the study of the asymptotic properties of backward self-similar solutions to the system together with the intersection comparison principle.
    Mathematics Subject Classification: Primary: 35K55, 35B40; Secondary: 34D05.

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