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Nonlinear Waves and Polarization in Diffusive Directed Particle Flow

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2018

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Fuhrmann, Jan

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https://doi.org/10.1137/17M1124103
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SIAM Journal on Applied Mathematics. 2018, 78(2), pp. 759-773. ISSN 0036-1399. eISSN 1095-712X. Available under: doi: 10.1137/17M1124103

Zusammenfassung

We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave solutions for weak diffusion by singular perturbation techniques and provide evidence for their existence also for stronger diffusion. We discuss different types of wave fronts and their composition into more complex patterns and illustrate the emergence of these patterns from generic initial data by simulations. We also investigate the dependence of the wave velocities on the model parameters.

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510 Mathematik

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ISO 690FREISTÜHLER, Heinrich, Jan FUHRMANN, 2018. Nonlinear Waves and Polarization in Diffusive Directed Particle Flow. In: SIAM Journal on Applied Mathematics. 2018, 78(2), pp. 759-773. ISSN 0036-1399. eISSN 1095-712X. Available under: doi: 10.1137/17M1124103
BibTex
@article{Freistuhler2018-01Nonli-42417,
  year={2018},
  doi={10.1137/17M1124103},
  title={Nonlinear Waves and Polarization in Diffusive Directed Particle Flow},
  number={2},
  volume={78},
  issn={0036-1399},
  journal={SIAM Journal on Applied Mathematics},
  pages={759--773},
  author={Freistühler, Heinrich and Fuhrmann, Jan}
}
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