Singular limits with vanishing viscosity for nonlocal conservation laws

2021 ◽  
Vol 211 ◽  
pp. 112370
Author(s):  
Giuseppe Maria Coclite ◽  
Nicola De Nitti ◽  
Alexander Keimer ◽  
Lukas Pflug
Keyword(s):  
Conservation Laws ◽  
Vanishing Viscosity ◽  
Singular Limits ◽  
Nonlocal Conservation Laws

scholarly journals A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

2018 ◽  
Vol 40 (1) ◽  
pp. 405-421 ◽  
Author(s):  
N Chatterjee ◽  
U S Fjordholm
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Examples ◽  
Continuity Equations ◽  
Multiple Dimensions ◽  
Nonlocal Conservation Laws ◽  
Volume Method ◽  
Singular Data

Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

scholarly journals Vanishing viscosity solutions for conservation laws with regulated flux

2019 ◽  
Vol 266 (1) ◽  
pp. 312-351 ◽  
Author(s):  
Alberto Bressan ◽  
Graziano Guerra ◽  
Wen Shen
Keyword(s):  
Conservation Laws ◽  
Viscosity Solutions ◽  
Vanishing Viscosity
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