Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux
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Fractional Keller-Segel, critical dissipation, bounded solutions, logistic dampeningAbstrakt
A semilinear version of parabolic-elliptic Keller--Segel system with the \emph{critical} nonlocal diffusion is considered in one space dimension. We show boundedness of weak solutions under very general conditions on our semilinearity. It can degenerate, but has to provide a stronger dissipation for large values of a solution than in the critical linear case or we need to assume certain (explicit) data smallness. Moreover, when one considers a~logistic term with a parameter $r$, we obtain our results even for diffusions slightly weaker than the critical linear one and for arbitrarily large initial datum, provided $r\ge 1$. For a mild logistic dampening, we can improve the smallness condition on the initial datum up to $\sim {1}/({1-r})$.Pobrania
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2016-03-01
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BURCZAK, Jan & GRANERO-BELINCHON, Rafael. Boundedness of large-time solutions to a chemotaxis model with nonlocal and semilinear flux. Topological Methods in Nonlinear Analysis [online]. 1 marzec 2016, T. 47, nr 1, s. 369–387. [udostępniono 22.7.2024].
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