Analysis and simulation of a nonlocal Gray-Scott model. (English) Zbl 1540.45016
This article presents a nonlocal Gray-Scott model posed on a bounded one-dimensional domain with Dirichlet and Neumann boundary conditions. The nonlocal operators are symmetric \(L^1\) convolution kernels that are also positive and spatially extended. The authors prove the existence of weak solutions for small time, and use a finite element method to investigate the effects of (exponential) nonlocal diffusion kernels on the formation of pulse solutions.
Reviewer: Joseph Shomberg (Providence)
MSC:
| 45K05 | Integro-partial differential equations |
| 45G15 | Systems of nonlinear integral equations |
| 46N20 | Applications of functional analysis to differential and integral equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 65R20 | Numerical methods for integral equations |
Keywords:
pattern formation; nonlocal diffusion; integro-differential equations; finite element methodReferences:
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