World Scientific Publishing, Mathematical Models and Methods in Applied Sciences, 12(26), p. 2311-2340
DOI: 10.1142/s0218202516500548
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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.