An aggregation equation with a nonlocal flux
Rafael Granero-Belinch\'on, Rafael Orive Illera
TL;DR
This paper investigates an aggregation equation with a nonlocal flux, analyzing conditions for well-posedness and global existence, and exploring how different nonlinearities affect the behavior through numerical simulations.
Contribution
It provides new insights into the well-posedness and global existence of solutions for aggregation equations with various nonlinear nonlocal fluxes, supported by numerical analysis.
Findings
Conditions for local well-posedness and global existence identified
Differences in solution behavior depending on nonlinearity convexity analyzed
Numerical simulations illustrate effects of nonlinearity changes
Abstract
In this paper we study an aggregation equation with a general nonlocal flux. We study the local well-posedness and some conditions ensuring global existence. We are also interested in the differences arising when the nonlinearity in the flux changes. Thus, we perform some numerics corresponding to different convexities for the nonlinearity in the equation.
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