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 journalArticle

7 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

Fingerprint

Euler-Poisson Equations
Critical Threshold
Large Time Behavior
Poisson equation
Damped
Damping
Classical Solution
Lagrangian Coordinates
Sharp Threshold
Mathematical Biology
Nonlocal Interactions
Collective Behavior
Breakdown
Asymptotic Behavior
Modeling

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

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On the pressureless damped Euler-Poisson equations with quadratic confinement : Critical thresholds and large-time behavior. / Carrillo, José A.; Choi, Young Pil; Zatorska, Ewelina.

In: Mathematical Models and Methods in Applied Sciences, Vol. 26, No. 12, 01.11.2016, p. 2311-2340.

Research output: Contribution to journalArticle

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