Stability of constant steady states of a chemotaxis model
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AbstractThe Cauchy problem for the parabolic–elliptic Keller–Segel system in the whole n-dimensional space is studied. For this model, every constant $$A \in {\mathbb {R}}$$ A ∈ R is a stationary solution. The main goal of this work is to show that $$A < 1$$ A < 1 is a stable steady state while $$A > 1$$ A > 1 is unstable. Uniformly local Lebesgue spaces are used in order to deal with solutions that do not decay at spatial variable on the unbounded domain.
2009 ◽
Vol 211
(2)
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pp. 374-382
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2005 ◽
Vol 42
(15)
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pp. 4338-4351
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2020 ◽
Vol 70
(2)
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pp. 77-83
1997 ◽
Vol 09
(06)
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pp. 675-687
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2015 ◽
Vol 37
(1)
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pp. 111-124
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