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We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a dampening effect on the model, are considered. Moreover, the system is characterized by nonlinear diffusion and sensitivity terms. We derive conditions on some data of the problem so to ensure the boundedness of related solutions. This work extends the research presented in Marras and Viglialoro (Math Nachr 291(14–15): 2318–2333 (2018), [19]), Columbu (J Math Anal Appl 546(1) (2025), [7]), where the same nonlinear model without gradient terms and its linear version with gradient sources has been, respectively, addressed.

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Boundedness in a Nonlinear Chemotaxis-Consumption Model with Gradient Terms

  • 会议论文

  • 发表日期：

    2026年

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  • Daniel Acosta-Soba,
  • Alessandro Columbu,
  • Giuseppe Viglialoro

摘要

We study a chemotaxis-consumption mechanism, in which some chemical signal and cells density interact each other. In order to control the concentration of such a population, sources involving gradient nonlinearities, which introduce a dampening effect on the model, are considered. Moreover, the system is characterized by nonlinear diffusion and sensitivity terms. We derive conditions on some data of the problem so to ensure the boundedness of related solutions. This work extends the research presented in Marras and Viglialoro (Math Nachr 291(14–15): 2318–2333 (2018), [19]), Columbu (J Math Anal Appl 546(1) (2025), [7]), where the same nonlinear model without gradient terms and its linear version with gradient sources has been, respectively, addressed.