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<p>This manuscript considers a spatial food chain model with alarm-taxis and singular sensitivity in a smoothly bounded plainer domain under zero-flux boundary conditions. Compared to the existing spatial food chain model, besides the complicated signal cascade mechanism, the possible prey-taxis singularity forms another challenge in analysis of the associated initial-boundary value problem. The gradient estimate of the primary predator density and the lower bound of the prey density are required to attain the global existence of solutions. By appropriate coupled energy estimates and an iterative procedure, based on the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2445_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^p-L^q\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>p</mi> </msup> <mo>-</mo> <msup> <mi>L</mi> <mi>q</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> estimates of Neumann heat semigroup, we establish the global existence of classical solutions, under a restriction on the prey-taxis coefficient.</p>

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Global existence of solutions to a three-species spatial food chain model with alarm-taxis and singular sensitivity

  • 期刊论文

  • 发表日期：

    2025年2月13日

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  • Yixuan Liu,
  • Li Xie

摘要

This manuscript considers a spatial food chain model with alarm-taxis and singular sensitivity in a smoothly bounded plainer domain under zero-flux boundary conditions. Compared to the existing spatial food chain model, besides the complicated signal cascade mechanism, the possible prey-taxis singularity forms another challenge in analysis of the associated initial-boundary value problem. The gradient estimate of the primary predator density and the lower bound of the prey density are required to attain the global existence of solutions. By appropriate coupled energy estimates and an iterative procedure, based on the \(L^p-L^q\) L p - L q estimates of Neumann heat semigroup, we establish the global existence of classical solutions, under a restriction on the prey-taxis coefficient.