We consider an advection-diffusion equation whose diffusivity can be negative. This equation arises in the modeling of collective movements, where the negative diffusivity simulates an aggregation behavior. Under suitable conditions we prove the existence, uniqueness and qualitative properties of traveling-wave solutions connecting states where the diffusivity has opposite signs. These results are extended to end states where the diffusivity is positive but is negative in between. The vanishing-viscosity limit is also considered. Examples from real-world models are provided.

Models of collective movements with negative degenerate diffusivities / Corli, Andrea; Malaguti, Luisa. - 10:(2020), pp. 393-399.

Models of collective movements with negative degenerate diffusivities

Luisa Malaguti
2020

Abstract

We consider an advection-diffusion equation whose diffusivity can be negative. This equation arises in the modeling of collective movements, where the negative diffusivity simulates an aggregation behavior. Under suitable conditions we prove the existence, uniqueness and qualitative properties of traveling-wave solutions connecting states where the diffusivity has opposite signs. These results are extended to end states where the diffusivity is positive but is negative in between. The vanishing-viscosity limit is also considered. Examples from real-world models are provided.
2020
Hyperbolic problems: theory, numerics, applications
A. Bressan, M. Lewicka, D. Wang, Y. Zeng
978-1-60133-023-9
1-60133-023-5
American Institute on Mathematical Sciences
STATI UNITI D'AMERICA
Models of collective movements with negative degenerate diffusivities / Corli, Andrea; Malaguti, Luisa. - 10:(2020), pp. 393-399.
Corli, Andrea; Malaguti, Luisa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1329595
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