Sharp viscous shock waves for relaxation model with degeneracy
This article is concerned with a relaxation model with degeneracy. Different from the existing studies on the regular viscous shock waves, we recognize that when the sub-characteristic condition is degenerate, the dynamical system possesses sharp viscous shock waves, a new type of viscous shock wave...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-08-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2025-0093 |
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| _version_ | 1849390289811144704 |
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| author | Xu Shufang Mei Ming Sheng Wancheng Wang Zejia |
| author_facet | Xu Shufang Mei Ming Sheng Wancheng Wang Zejia |
| author_sort | Xu Shufang |
| collection | DOAJ |
| description | This article is concerned with a relaxation model with degeneracy. Different from the existing studies on the regular viscous shock waves, we recognize that when the sub-characteristic condition is degenerate, the dynamical system possesses sharp viscous shock waves, a new type of viscous shock waves with sharp corners and being regionally degenerate in a half space. The regularities of these sharp viscous shock waves are further derived. Some of them can be smooth due to different degree of degeneracy, but most of them are Hölder continuous with sharp corners. Finally, the exact sharp viscous shock waves are constructed for three typical equations, and the corresponding numerical simulations with given initial data are also presented, which perfectly match the exact sharp viscous shock waves and also numerically demonstrate the stability of sharp shock waves. |
| format | Article |
| id | doaj-art-c7fc0b817dd14f14a00f2c0f4be7071f |
| institution | Kabale University |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-c7fc0b817dd14f14a00f2c0f4be7071f2025-08-20T03:41:43ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-08-01141p. 16117610.1515/anona-2025-0093Sharp viscous shock waves for relaxation model with degeneracyXu Shufang0Mei Ming1Sheng Wancheng2Wang Zejia3Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. ChinaSchool of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, P. R. ChinaDepartment of Mathematics, Shanghai University, Shanghai, 200444, P. R. ChinaSchool of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, P. R. ChinaThis article is concerned with a relaxation model with degeneracy. Different from the existing studies on the regular viscous shock waves, we recognize that when the sub-characteristic condition is degenerate, the dynamical system possesses sharp viscous shock waves, a new type of viscous shock waves with sharp corners and being regionally degenerate in a half space. The regularities of these sharp viscous shock waves are further derived. Some of them can be smooth due to different degree of degeneracy, but most of them are Hölder continuous with sharp corners. Finally, the exact sharp viscous shock waves are constructed for three typical equations, and the corresponding numerical simulations with given initial data are also presented, which perfectly match the exact sharp viscous shock waves and also numerically demonstrate the stability of sharp shock waves.https://doi.org/10.1515/anona-2025-0093relaxation modelsharp viscous shock wavesregularitydegeneracy35l6735l8176l05 |
| spellingShingle | Xu Shufang Mei Ming Sheng Wancheng Wang Zejia Sharp viscous shock waves for relaxation model with degeneracy Advances in Nonlinear Analysis relaxation model sharp viscous shock waves regularity degeneracy 35l67 35l81 76l05 |
| title | Sharp viscous shock waves for relaxation model with degeneracy |
| title_full | Sharp viscous shock waves for relaxation model with degeneracy |
| title_fullStr | Sharp viscous shock waves for relaxation model with degeneracy |
| title_full_unstemmed | Sharp viscous shock waves for relaxation model with degeneracy |
| title_short | Sharp viscous shock waves for relaxation model with degeneracy |
| title_sort | sharp viscous shock waves for relaxation model with degeneracy |
| topic | relaxation model sharp viscous shock waves regularity degeneracy 35l67 35l81 76l05 |
| url | https://doi.org/10.1515/anona-2025-0093 |
| work_keys_str_mv | AT xushufang sharpviscousshockwavesforrelaxationmodelwithdegeneracy AT meiming sharpviscousshockwavesforrelaxationmodelwithdegeneracy AT shengwancheng sharpviscousshockwavesforrelaxationmodelwithdegeneracy AT wangzejia sharpviscousshockwavesforrelaxationmodelwithdegeneracy |