Stability of peak solutions of a non-linear transport equation on the circle

Details Stability of peak solutions of a non-linear transport equation on the circle Stability of peak solutions of a non-linear transport equation on the circle

2011-08-27

arxiv.org/abs/1108.5462v2

Mathematics

Analysis of PDEs

39 pages, 6 figures; version 2: small clarification related to one of the examples in Figure 5

Scientific paper

We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit for vanishing diffusion, linear combinations of delta peaks can be stationary solutions; we study their stability properties. Finally, we present numerical examples exhibiting a variety of behaviors.

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