• Corpus ID: 18684226

STABILITY OF PEAK SOLUTIONS OF A NON-LINEAR TRANSPORT EQUATION ON THE CIRCLE

@article{Geigant2012STABILITYOP,
  title={STABILITY OF PEAK SOLUTIONS OF A NON-LINEAR TRANSPORT EQUATION ON THE CIRCLE},
  author={Edith Geigant and Michael Stoll},
  journal={arXiv: Analysis of PDEs},
  year={2012}
}
We study solutions of a transport-diusio n equation on the circle. The velocity of turning is given by a non-local term that models attraction and repulsion between elongated particles. Having mentioned basics like invariances, instability criteria and non-existence of time-periodic solutions, we prove that the constant steady state is stable at large diusion. We show that without diusion localized initial distributions and attraction lead to formation of several peaks. For peak-like steady… 

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