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<p>This paper is concerned with the asymptotic profiles and sharp patterns of positive solutions to a degenerate and mixed reaction-diffusion equation. It is shown that the interplay among spatial degeneracy, nonlocal, and the nonlinear reaction function induce fundamental alterations in the asymptotic behavior of positive solutions. Moreover, our analysis reveals that the nonlinearity can effectively suppress nonlocal effects, leading to the emergence of two distinct blow-up rates that govern the sharp asymptotic patterns.</p>

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Sharp asymptotic profiles of positive solutions to degenerate mixed local-nonlocal diffusion equations

  • 期刊论文

  • 发表日期：

    2026年5月29日

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  • Jian-Wen Sun,
  • Wen-Jing Chang,
  • Willian Cintra

摘要

This paper is concerned with the asymptotic profiles and sharp patterns of positive solutions to a degenerate and mixed reaction-diffusion equation. It is shown that the interplay among spatial degeneracy, nonlocal, and the nonlinear reaction function induce fundamental alterations in the asymptotic behavior of positive solutions. Moreover, our analysis reveals that the nonlinearity can effectively suppress nonlocal effects, leading to the emergence of two distinct blow-up rates that govern the sharp asymptotic patterns.