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.
Nonlocal Conservation Laws in Bounded Domains / Colombo, Rm; Rossi, E. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 50:4(2018), pp. 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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