On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior

José A. Carrillo, Young Pil Choi, Ewelina Zatorska

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We analyze the one-dimensional pressureless Euler-Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling 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.

Original languageEnglish
Pages (from-to)2311-2340
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Volume26
Issue number12
DOIs
Publication statusPublished - 2016 Nov 1

Bibliographical note

Funding Information:
J.A.C. and Y.P.C. were partially supported by EPSRC Grant EP/K008404/1. E.Z. has been partly supported by the National Science Center Grant 2014/14/M/ST1/00108 (Harmonia).

Publisher Copyright:
© 2016 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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