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Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source

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Abstract

We study the chemotaxis system with singular sensitivity and logistic-type source: ut = Δu − χ∇ · (u∇v/v) + ru − μuk, 0 = Δv − v + u under the non-flux boundary conditions in a smooth bounded domain Ω ⊂ ℝn, χ, r, μ > 0, k > 1 and n ⩾ 1. It is shown with k ∈ (1, 2) that the system possesses a global generalized solution for n ⩾ 2 which is bounded when χ > 0 is suitably small related to r > 0 and the initial datum is properly small, and a global bounded classical solution for n = 1.

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Authors and Affiliations

  1. School of Mathematics, Liaoning Normal University, No.850 Huanghe Road Shahekou District, Dalian, 116029, P. R. China

    Xiangdong Zhao

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  1. Xiangdong Zhao
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Correspondence to Xiangdong Zhao.

Additional information

This work was supposed by the Doctoral Scientific Research Foundation of Liaoning Normal University (Grant No. 203070091907), the Doctoral Scientific Research Foundation of Liaoning Science and Technology Department (Grant No. 2020-BS-185).

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Zhao, X. Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source. Czech Math J 74, 127–151 (2024). https://doi.org/10.21136/CMJ.2023.0544-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0544-22

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