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 |
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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 |
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