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Abstract <p> We study nonlinear reaction-diffusion equations with non-local source terms, in which the results arise in population dynamics and epidemiology. Under mild conditions on the initial data, interaction kernel, and nonlinearity, we prove the existence, uniqueness, and positivity of bounded classical solutions. The analysis employs a Hammerstein-Volterra nonlinear integral formulation and a constructive monotone iteration scheme that preserves positivity and continuity. Special cases with vanishing reproduction rate and constant source intensity on finite time intervals are also investigated. The results extend known one-dimensional models to a general multidimensional framework. </p>

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Existence and Uniqueness of Solutions to Non-Local Nonlinear Reaction-Diffusion Equations

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Zahra Keyshams,
  • Khachatur Khachatryan

摘要

Abstract

We study nonlinear reaction-diffusion equations with non-local source terms, in which the results arise in population dynamics and epidemiology. Under mild conditions on the initial data, interaction kernel, and nonlinearity, we prove the existence, uniqueness, and positivity of bounded classical solutions. The analysis employs a Hammerstein-Volterra nonlinear integral formulation and a constructive monotone iteration scheme that preserves positivity and continuity. Special cases with vanishing reproduction rate and constant source intensity on finite time intervals are also investigated. The results extend known one-dimensional models to a general multidimensional framework.