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.
|Number of pages||30|
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2016 Nov 1|
Bibliographical noteFunding 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).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics