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<p>This paper investigates the global boundedness of classical solutions to a class of chemotaxis models proposed to describe the response of cytotoxic T-lymphocytes (CTLs) to a solid tumor. Under homogeneous Neumann boundary conditions on a smooth bounded domain, we prove that for spatial dimension <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(1\le N\le 7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>N</mi> <mo>≤</mo> <mn>7</mn> </mrow> </math></EquationSource> </InlineEquation>, the system admits global bounded classical solutions. In particular, for dimensions <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(4\le N \le 7\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mo>≤</mo> <mi>N</mi> <mo>≤</mo> <mn>7</mn> </mrow> </math></EquationSource> </InlineEquation>, we develop a novel double-iteration technique to establish the required boundedness.</p>

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Boundedness of classical solutions for a chemotaxis model with nonlinear signal production

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Jiashan Zheng,
  • Yongxiu Shi

摘要

This paper investigates the global boundedness of classical solutions to a class of chemotaxis models proposed to describe the response of cytotoxic T-lymphocytes (CTLs) to a solid tumor. Under homogeneous Neumann boundary conditions on a smooth bounded domain, we prove that for spatial dimension \(1\le N\le 7\) 1 ≤ N ≤ 7 , the system admits global bounded classical solutions. In particular, for dimensions \(4\le N \le 7\) 4 ≤ N ≤ 7 , we develop a novel double-iteration technique to establish the required boundedness.