Blow-up versus global existence of solutions to aggregation equations

Abstract

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. Optimal conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.

References in corpus (2)

• Blowup of solutions to a diffusive aggregation model
• Blow up of solutions to generalized Keller--Segel model

Cited by in corpus (3)

• Inhomogeneous Patlak-Keller-Segel models and Aggregation Equations with Nonlinear Diffusion in $\Real^d$
• Large mass global solutions for a class of L1-critical nonlocal aggregation equations and parabolic-elliptic Patlak-Keller-Segel models
• Asymptotics behaviour in one dimensional model of interacting particles