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<p>This paper concerns with steady states and their attraction basins of KPP and bistable type reaction-diffusion equations subject to the Dirichlet condition on the boundary of unbounded sectors. First, by the sliding-sector method, maximum principle, and Harnack inequality, we describe the shape and attraction basins of axial symmetric heterogeneous steady states for the case involving a KPP type reaction term in unbounded sectors. Then, based on these results and parabolic regularity estimates up to smooth boundary parts, we describe the multiplicity, shape, and attractivity of axial symmetric heterogeneous steady states for bistable reaction-diffusion equations on unbounded sectors and the plane. Our work recovers some results on some nonlinear heat equations on special unbounded sectors, which were obtained via quite different approaches.</p>

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Steady States for KPP/Bistable Type Equations on Unbounded Sectors and their Attraction Basins

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Jing Chen,
  • Yuming Chen,
  • Jianhong Wu,
  • Taishan Yi

摘要

This paper concerns with steady states and their attraction basins of KPP and bistable type reaction-diffusion equations subject to the Dirichlet condition on the boundary of unbounded sectors. First, by the sliding-sector method, maximum principle, and Harnack inequality, we describe the shape and attraction basins of axial symmetric heterogeneous steady states for the case involving a KPP type reaction term in unbounded sectors. Then, based on these results and parabolic regularity estimates up to smooth boundary parts, we describe the multiplicity, shape, and attractivity of axial symmetric heterogeneous steady states for bistable reaction-diffusion equations on unbounded sectors and the plane. Our work recovers some results on some nonlinear heat equations on special unbounded sectors, which were obtained via quite different approaches.