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
Saturated Fronts in Crowds Dynamics / Campos, Juan; Corli, Andrea; Malaguti, Luisa. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 21:2(2021), pp. 303-326. [10.1515/ans-2021-2118]
Saturated Fronts in Crowds Dynamics
Malaguti, Luisa
Membro del Collaboration Group
2021
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
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