Stability of solutions to aggregation equation in bounded domains

Rafał Celiński

Stability of solutions to aggregation equation in bounded domains

Analysis of PDEs 2013-03-20 v2

Authors: Rafał Celiński

Abstract

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.

Keywords

aggregation equation bounded domains Neumann boundary condition integral operator local existence global existence stability instability

Cite

@article{arxiv.1204.5293,
  title  = {Stability of solutions to aggregation equation in bounded domains},
  author = {Rafał Celiński},
  journal= {arXiv preprint arXiv:1204.5293},
  year   = {2013}
}

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