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<p>This paper investigates the existence of traveling wave solutions for diffusive two-species Lotka–Volterra systems with delays in both the reaction and diffusion terms under partial monotonicity assumptions. The model incorporates small-memory effects in the homogeneous diffusion term, representing a modification of the random-walk interpretation underlying Fick’s law. We extend the partial (cross) monotone iteration method to systems satisfying a partial quasi-monotone condition through the construction of appropriate upper and lower solutions. Convergence of the iteration is established using Schauder’s fixed point theorem.</p>

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Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity

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  • 发表日期：

    2026年5月4日

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  • William Barker

摘要

This paper investigates the existence of traveling wave solutions for diffusive two-species Lotka–Volterra systems with delays in both the reaction and diffusion terms under partial monotonicity assumptions. The model incorporates small-memory effects in the homogeneous diffusion term, representing a modification of the random-walk interpretation underlying Fick’s law. We extend the partial (cross) monotone iteration method to systems satisfying a partial quasi-monotone condition through the construction of appropriate upper and lower solutions. Convergence of the iteration is established using Schauder’s fixed point theorem.