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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2020

MASS THRESHOLD FOR INFINITE-TIME BLOWUP IN A CHEMOTAXIS MODEL WITH SPLIT POPULATION

Christian Stinner
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Résumé

We study the chemotaxis model ∂ t u = div(∇u − u∇w) + θv − u in (0, ∞) × Ω, ∂ t v = u − θv in (0, ∞) × Ω, ∂ t w = D∆w − αw + v in (0, ∞) × Ω, with no-flux boundary conditions in a bounded and smooth domain Ω ⊂ R 2 , where u and v represent the densities of subpopulations of moving and static individuals of some species, respectively, and w the concentration of a chemoattractant. We prove that, in an appropriate functional setting, all solutions exist globally in time. Moreover, we establish the existence of a critical mass M c > 0 of the whole population u + v such that, for M ∈ (0, M c), any solution is bounded, while, for almost all M > M c , there exist solutions blowing up in infinite time. The building block of the analysis is the construction of a Liapunov functional. As far as we know, this is the first result of this kind when the mass conservation includes the two subpopulations and not only the moving one.
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Dates et versions

hal-02943355 , version 1 (19-09-2020)
hal-02943355 , version 2 (28-09-2021)

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Philippe Laurençot, Christian Stinner. MASS THRESHOLD FOR INFINITE-TIME BLOWUP IN A CHEMOTAXIS MODEL WITH SPLIT POPULATION. SIAM Journal on Mathematical Analysis, 2020, 53 (3), pp.3385--3419. ⟨hal-02943355v2⟩
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