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A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

  • José A. Carrillo (a1), Alina Chertock (a2) and Yanghong Huang (a1)


We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics demonstrated by suitably chosen test cases in which these features of the scheme are essential. The proposed scheme is able to cope with non-smooth stationary states, different time scales including metastability, as well as concentrations and self-similar behavior induced by singular nonlocal kernels. We use the scheme to explore properties of these equations beyond their present theoretical knowledge.


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*Email A. Carrillo), Cherock), Huang)


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A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

  • José A. Carrillo (a1), Alina Chertock (a2) and Yanghong Huang (a1)


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