| Abstract: |
| In this talk, we study the mathematical relationship between nonlocal interactions of convolution type and systems of multiple diffusive substances in high-dimensional space. Motivated by the observation that nonlocal evolution equations can reproduce similar patterns to those arising in reaction-diffusion systems, we approximate nonlocal interactions in evolution equations by solutions to appropriate reaction-diffusion systems with multiple components in Euclidean space of arbitrary dimension. It is shown that any absolutely integrable radial kernel can be approximated by a linear combination of specific Green functions to elliptic partial differential equations. This enables us to demonstrate that a linear sum of auxiliary diffusive substances can approximate a broad class of nonlocal interactions of convolution type. Our results establish a connection between a broad class of nonlocal interactions and diffusive chemical reactions in dynamical systems. |
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