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 |
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics
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Carrillo, J. A., Choi, Y. P., & 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), 2311-2340. https://doi.org/10.1142/S0218202516500548