Carrillo, JA;
Choi, YP;
Zatorska, E;
(2016)
On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior.
Mathematical Models and Methods in Applied Sciences
, 26
(12)
pp. 2311-2340.
10.1142/S0218202516500548.
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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.
Type: | Article |
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Title: | On the pressureless damped Euler-Poisson equations with quadratic confinement: Critical thresholds and large-time behavior |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1142/S0218202516500548 |
Publisher version: | https://doi.org/10.1142/S0218202516500548 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Flocking; alignment; hydrodynamics; regularity; critical thresholds |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
URI: | https://discovery.ucl.ac.uk/id/eprint/10035987 |
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