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On a Keller-Segel system with logarithmic sensitivity and non-diffusive chemical

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  • We consider a chemotactic system with a logarithmic sensitivity and a non-diffusing chemical. We establish local regular solutions in time and give some characterizations on parameters and initial data for global solutions and blow-up in a finite time. We also prove that there does not exist finite time self-similar solution of the backward type.
    Mathematics Subject Classification: Primary: 35K57, 35Q92; Secondary: 92C17.


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