BooksecrCollected Volumepp. 101–133

Deterministic particle method for nonlinear nonlocal scalar balance equations

  • Emanuela Radici

    Università degli Studi dell’Aquila, L’Aquila, Italy

  • Federico Stra

    Politecnico di Torino, Italy
Deterministic particle method for nonlinear nonlocal scalar balance equations cover
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Abstract

We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to Radici–Stra [SIAM J. Math. Anal. 55 (2023), no. 3, 2001–2041] is the presence of a source term; this causes the solutions to no longer be probability measures, thus requiring a suitable adaptation of the numerical scheme and of the estimates leading to compactness.