Stability of solutions to aggregation equation in a bounded domains

Details Stability of solutions to aggregation equation in a bounded domains Stability of solutions to aggregation equation in a bounded domains

2012-04-24

arxiv.org/abs/1204.5293v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the aggregation equation $u_t= \div(\nabla u-u\nabla \K(u))$ in a bounded domain $\Omega\subset \R^d$ 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.

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