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<p>This paper investigates the existence and uniqueness of traveling wave solutions for nonlocal diffusion equations with sign-changing kernel and spatio-temporal delays. We first obtain the existence of traveling waves using upper–lower solutions method and Schauder’s fixed point theorem for any <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c&gt;c^{**}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>&gt;</mo> <msup> <mi>c</mi> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(c^{**}&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>c</mi> <mrow> <mrow /> <mo>∗</mo> <mrow /> <mo>∗</mo> </mrow> </msup> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> is a constant. Second, we analyze the asymptotic behavior of the wave profile at positive infinity. We further prove that for large wave speeds, there exist traveling waves connecting 0 and <i>K</i>. Finally, we establish the uniqueness of the traveling wave solutions up to translation.</p>

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Traveling waves for nonlocal diffusion equations with a sign-changing kernel and spatio-temporal delays

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Zikang Fan,
  • Jiaqi Yang,
  • Jiaojiao Wang

摘要

This paper investigates the existence and uniqueness of traveling wave solutions for nonlocal diffusion equations with sign-changing kernel and spatio-temporal delays. We first obtain the existence of traveling waves using upper–lower solutions method and Schauder’s fixed point theorem for any \(c>c^{**}\) c > c ∗ ∗ , where \(c^{**}>0\) c ∗ ∗ > 0 is a constant. Second, we analyze the asymptotic behavior of the wave profile at positive infinity. We further prove that for large wave speeds, there exist traveling waves connecting 0 and K. Finally, we establish the uniqueness of the traveling wave solutions up to translation.