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Global solvability in a Keller-Segel-growth system with indirect signal production

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Abstract

In this paper, we consider a fully parabolic Keller-Segel-growth system with indirect signal production: \(u_t=\Delta u-\chi \nabla \cdot (u\nabla v)+f(u)\); \(v_t=\Delta v-v+w\); \(w_t=\Delta w-w+u\), \(x\in \Omega \), \(t>0\) in a bounded and smooth domain \(\Omega \subset {\mathbb {R}}^N\) \((N\ge 2)\) with no-flux boundary conditions, where \(\chi \) is a positive constant. We present the global existence of generalized solutions under appropriate regularity assumptions on the initial data. In addition, the asymptotic behavior of generalized solutions is discussed, and our result generalize previously known ones.

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Acknowledgements

The author would like to thank Professor Michael Winkler for sharing his preprint [51] and express his gratitude to Professor Bin Liu for helpful discussions during the preparation of the paper as well as the anonymous reviewers and editors for their valuable comments and suggestions which led to the improvement of the original manuscript. Guoqiang Ren is partially supported by the National Natural Science Foundation of China (No. 12001214) and the Fundamental Research Funds for the Central Universities (Grant No. 3004011139).

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  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Guoqiang Ren

  2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Guoqiang Ren

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Ren, G. Global solvability in a Keller-Segel-growth system with indirect signal production. Calc. Var. 61, 207 (2022). https://doi.org/10.1007/s00526-022-02313-5

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