On the pressureless damped Euler-Poisson equations with non-local forces: Critical thresholds and large-time behavior

2016/04/18 by José A. Carrillo, Carrillo, José A., Young-Pil Choi +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1604.05229

arxiv created 2016/04/18 · arxiv updated 2016/04/19

Abstract

We analyse the one-dimensional pressureless Euler-Poisson equations with a linear damping and non-local interaction forces. These equations are relevant for modelling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an explicit form of solution in Lagrangian coordinates which enables us to study the time-asymptotic behavior of classical solutions with the initial data in the subcritical region.

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