Stability of solutions to aggregation equation in bounded domains

摘要

We consider the aggregation equation ut=∇·(∇u-u∇K(u)) in a bounded domain Ω⊂Rd with supplemented the Neumann boundary condition and with a nonnegative, integrable initial datum. Here, K=K(u) is an integral operator. We study the local and global existence of solutions and we derive conditions which lead us to either the stability or instability of constant solutions.