Saturated Fronts in Crowds Dynamics-Reference-Cited by-同舟云学术

Saturated Fronts in Crowds Dynamics

Published:2021-02-02 Issue:2 Volume:21 Page:303-326
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Campos Juan¹^ORCID,Corli Andrea²^ORCID,Malaguti Luisa³^ORCID

Affiliation:

1. Department of Applied Mathematics , University of Granada , Granada , Spain

2. Department of Mathematics and Computer Science , University of Ferrara , Ferrara , Italy

3. Department of Sciences and Methods for Engineering , University of Modena and Reggio Emilia , Modena , Italy

Abstract

Abstract We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be discontinuous. Uniqueness is recovered by requiring an entropy condition, and entropic solutions turn out to be the vanishing-diffusion limits of traveling-wave solutions to the equation with an additional non-degenerate diffusion. Applications to crowds dynamics, which motivated the present research, are also provided.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2021-2118/pdf

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