The well posedness for a class of nonlocal systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modeling of crowd dynamics, which also leads to defining a nonlocal operator adapted to the presence of a boundary. Numerical integrations show that the resulting model provides qualitatively reasonable solutions.
Colombo, R., Rossi, E. (2018). Nonlocal Conservation Laws in Bounded Domains. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 50(4), 4041-4065 [10.1137/18M1171783].
Nonlocal Conservation Laws in Bounded Domains
Rossi, E
2018
Abstract
The well posedness for a class of nonlocal systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modeling of crowd dynamics, which also leads to defining a nonlocal operator adapted to the presence of a boundary. Numerical integrations show that the resulting model provides qualitatively reasonable solutions.
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