Saturated Fronts in Crowds Dynamics
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 requ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-05-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2021-2118 |
| _version_ | 1811185935480520704 |
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| author | Campos Juan Corli Andrea Malaguti Luisa |
| author_facet | Campos Juan Corli Andrea Malaguti Luisa |
| author_sort | Campos Juan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T13:37:50Z |
| format | Article |
| id | doaj.art-97367a00c7a5485393b136674d5e89d6 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-11T13:37:50Z |
| publishDate | 2021-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-97367a00c7a5485393b136674d5e89d62022-12-22T04:21:24ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752021-05-0121230332610.1515/ans-2021-2118Saturated Fronts in Crowds DynamicsCampos Juan0Corli Andrea1Malaguti Luisa2Department of Applied Mathematics, University of Granada, Granada, SpainDepartment of Mathematics and Computer Science, University of Ferrara, Ferrara, ItalyDepartment of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Modena, ItalyWe 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.https://doi.org/10.1515/ans-2021-2118traveling-wave solutionsentropic solutionsnonlinear convection-diffusion equations35k65 35c07 35k57 |
| spellingShingle | Campos Juan Corli Andrea Malaguti Luisa Saturated Fronts in Crowds Dynamics Advanced Nonlinear Studies traveling-wave solutions entropic solutions nonlinear convection-diffusion equations 35k65 35c07 35k57 |
| title | Saturated Fronts in Crowds Dynamics |
| title_full | Saturated Fronts in Crowds Dynamics |
| title_fullStr | Saturated Fronts in Crowds Dynamics |
| title_full_unstemmed | Saturated Fronts in Crowds Dynamics |
| title_short | Saturated Fronts in Crowds Dynamics |
| title_sort | saturated fronts in crowds dynamics |
| topic | traveling-wave solutions entropic solutions nonlinear convection-diffusion equations 35k65 35c07 35k57 |
| url | https://doi.org/10.1515/ans-2021-2118 |
| work_keys_str_mv | AT camposjuan saturatedfrontsincrowdsdynamics AT corliandrea saturatedfrontsincrowdsdynamics AT malagutiluisa saturatedfrontsincrowdsdynamics |