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A Numerical Method for a 1-d Nonlocal Gray Scott Model

Gabriela Jaramillo
University of Houston


The Gray Scott model is a set of reaction diffusion equations known to generate a wide variety of patterns. In this talk we consider a version of this model where diffusion is assumed to be nonlocal and can be described by convolution kernels that decay exponentially at infinity and have finite second moment. We prove the local well-posedness of the model on bounded one-dimensional domains with nonlocal Dirichlet and Neumann boundary constraints. We also present a numerical scheme that uses a quadrature-based finite difference to discretize the convolution operator. We show how the scheme allows us to approximate solutions to the nonlocal Gray Scott model both on bounded and unbounded domains.

Tuesday, April 26, 2022
11:00AM Zoom ID 954 6624 3503