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Convergence rate estimates of a higher-dimension reaction–diffusion system with density-dependent motility

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Abstract

This paper deals with a three-component parabolic system with density-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a higher-dimensional smoothly bounded domain. This system was used to describe the dynamics of a population of cells interacting with a chemoattractant and a nutrient. Based on the method of energy estimates and Moser iteration, we establish the global boundedness and the time-decay rates of the classical solutions under suitable conditions. This results perfect the corresponding results in Jin et al. (J Differ Equ 269:6758–6793, 2020).

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Acknowledgements

This work is partially supported by the NSFC (Grant No. 11971082), the Chongqing Talent Support program (Grant No. cstc2022ycjh-bgzxm0169), Natural Science Foundation of Chongqing (Grant No. cstc2021jcyj-msxmX1051), the Fundamental Research Funds for the Central Universities (Grant Nos. 2020CDJQY-Z001, 2019CDJCYJ001), and Chongqing Key Laboratory of Analytic Mathematics and Applications.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Yafeng Li & Chunlai Mu

  2. College of Mathematics and Statistics, Yili Normal University, Yining, 835000, People’s Republic of China

    Qiao Xin

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  1. Yafeng Li
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  2. Chunlai Mu
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Correspondence to Yafeng Li.

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Li, Y., Mu, C. & Xin, Q. Convergence rate estimates of a higher-dimension reaction–diffusion system with density-dependent motility. Z. Angew. Math. Phys. 73, 146 (2022). https://doi.org/10.1007/s00033-022-01762-4

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  • DOI: https://doi.org/10.1007/s00033-022-01762-4

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