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

José A. Carrillo; Young Pil Choi; Ewelina Zatorska

doi:10.1142/S0218202516500548

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

José A. Carrillo, Young Pil Choi, Ewelina Zatorska

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

23 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 language	English
Pages (from-to)	2311-2340
Number of pages	30
Journal	Mathematical Models and Methods in Applied Sciences
Volume	26
Issue number	12
DOIs	https://doi.org/10.1142/S0218202516500548
Publication status	Published - 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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10.1142/S0218202516500548

Cite this

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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.",

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N1 - 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.

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AB - 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.

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

Abstract

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