Deterministic particle method for nonlinear nonlocal scalar balance equations

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. 55.3 (2023)]" 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.

26 pages, 1 figure