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 | |
| Publication status | Published - 2016 Nov 1 |
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - On the pressureless damped Euler-Poisson equations with quadratic confinement
T2 - Critical thresholds and large-time behavior
AU - Carrillo, José A.
AU - Choi, Young Pil
AU - Zatorska, Ewelina
PY - 2016/11/1
Y1 - 2016/11/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84989233667&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84989233667&partnerID=8YFLogxK
U2 - 10.1142/S0218202516500548
DO - 10.1142/S0218202516500548
M3 - Article
AN - SCOPUS:84989233667
VL - 26
SP - 2311
EP - 2340
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 12
ER -