In this talk, we consider reaction-diffusion equations with nonlocal effect described by the convolution in the spatial direction of the unknown function and the integral kernel. Such nonlocal effects are often used to describe nonlocal diffusion effects of substances, cell-cell interactions, etc. To consider pattern formation in nonlocal reaction-diffusion equations, we present results of mathematical analysis on the dynamics of localized patterns. We mainly introduce results on the behavior of phase-separated patterns when the nonlocal effect is sufficiently weak. The influence of the integral kernel shapes in the situation will be reviewed, and the influence of nonlocal effects on pattern formation will be discussed.

 

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