Approximation of viscous transport and conservative equations with one sided Lipschitz velocity fields

2025/05/13 by Camilli, Fabio, Festa, Adriano, Marzufero, Luciano
#35D30 #35K20 #49L25 #65M12 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2505.08970

Abstract

The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent viscosity solution and, respectively, duality solution. We supplement our theoretical analysis with various numerical examples to illustrate the features of the schemes.

Citations

• Transport equations and flows with one-sided Lipschitz velocity fields
• Conservation laws with discontinuous flux function on networks: a splitting algorithm
• On first order mean field game systems with a common noise
• A model for a network of conveyor belts with discontinuous speed and\n capacity
• On the discretization of some nonlinear Fokker-Planck-Kolmogorov\n equations and applications
• Convergence order of upwind type schemes for transport equations with\n discontinuous coefficients
• Semi-Lagrangian methods for parabolic problems in divergence form
• A Semi-Lagrangian scheme for a degenerate second order Mean Field Game\n system
• Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient
• An approximation scheme for the optimal control of diffusion processes

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