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<p>This paper is concerned with the Neumann initial-boundary problems for singular chemotaxis systems with nonlinear production of environmental cues. Based on approximation by solutions to regularized variants, a conditional result on the existence of large-data global generalized solutions to this problem is established. Particular applications of this general theory are seen to provide unconditional existence results for systems modeling dynamics of urban crime and epidemic spreading.</p>

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A unified approach to existence theories for singular chemotaxis systems with nonlinear signal production

  • 期刊论文

  • 发表日期：

    2025年7月23日

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  • Youshan Tao,
  • Michael Winkler

摘要

This paper is concerned with the Neumann initial-boundary problems for singular chemotaxis systems with nonlinear production of environmental cues. Based on approximation by solutions to regularized variants, a conditional result on the existence of large-data global generalized solutions to this problem is established. Particular applications of this general theory are seen to provide unconditional existence results for systems modeling dynamics of urban crime and epidemic spreading.