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<p>In this paper, our goal is to research propagation phenomena of spatially periodic combustion reaction-diffusion equations in an exterior domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega =\mathbb {R}^N\backslash K\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>=</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> <mrow> <mo stretchy="true">\</mo> <mi>K</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation>, where the compact set <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(K\subset \mathbb {R}^{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>K</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> stands for an obstacle. We establish the existence of pulsating front-like solutions originating from a spatially periodic combustion pulsating front in the exterior domain <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>. In particular, distinguished from the bistable models, the propagation of the pulsating front-like solutions is always complete (i.e., local convergence to 1), which does not depend on the geometric structure of the obstacle <i>K</i>. Also, the pulsating front-like solution is unique, and will gradually recover to the exactly same pulsating front after getting remote from the obstacle <i>K</i>.</p>

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Pulsating front-like solutions of spatially periodic combustion reaction-diffusion equations in exterior domains

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Fu-Jie Jia,
  • Yu-Chao Ma,
  • Xiongxiong Bao,
  • Gai-Hui Guo

摘要

In this paper, our goal is to research propagation phenomena of spatially periodic combustion reaction-diffusion equations in an exterior domain \(\Omega =\mathbb {R}^N\backslash K\) Ω = R N \ K , where the compact set \(K\subset \mathbb {R}^{N}\) K ⊂ R N stands for an obstacle. We establish the existence of pulsating front-like solutions originating from a spatially periodic combustion pulsating front in the exterior domain \(\Omega \) Ω . In particular, distinguished from the bistable models, the propagation of the pulsating front-like solutions is always complete (i.e., local convergence to 1), which does not depend on the geometric structure of the obstacle K. Also, the pulsating front-like solution is unique, and will gradually recover to the exactly same pulsating front after getting remote from the obstacle K.