Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks
In this article, we study the inviscid limit of the solution to the Cauchy problem of a one-dimensional viscous conservation law, where the second-order term is nonlinear. Under the assumption that the inviscid equation admits a piecewise smooth solution with two noninteracting entropy shocks, we pr...
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| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0080 |
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| author | Feng Li Wang Jing |
| author_facet | Feng Li Wang Jing |
| author_sort | Feng Li |
| collection | DOAJ |
| description | In this article, we study the inviscid limit of the solution to the Cauchy problem of a one-dimensional viscous conservation law, where the second-order term is nonlinear. Under the assumption that the inviscid equation admits a piecewise smooth solution with two noninteracting entropy shocks, we prove that the solution of the viscous equation converges uniformly to the piecewise smooth inviscid solution away from the shocks, even the strength of shocks is not small. |
| format | Article |
| id | doaj-art-ea30459a3f184177ba1e2d75a86016ef |
| institution | DOAJ |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-ea30459a3f184177ba1e2d75a86016ef2025-08-20T02:50:48ZengDe GruyterDemonstratio Mathematica2391-46612024-11-0157127729810.1515/dema-2024-0080Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocksFeng Li0Wang Jing1Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. ChinaIn this article, we study the inviscid limit of the solution to the Cauchy problem of a one-dimensional viscous conservation law, where the second-order term is nonlinear. Under the assumption that the inviscid equation admits a piecewise smooth solution with two noninteracting entropy shocks, we prove that the solution of the viscous equation converges uniformly to the piecewise smooth inviscid solution away from the shocks, even the strength of shocks is not small.https://doi.org/10.1515/dema-2024-0080shock layerviscous shocksmatched asymptotic expansionnonlinear stabilityenergy estimates35l5035l6035l6535k5935k65 |
| spellingShingle | Feng Li Wang Jing Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks Demonstratio Mathematica shock layer viscous shocks matched asymptotic expansion nonlinear stability energy estimates 35l50 35l60 35l65 35k59 35k65 |
| title | Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks |
| title_full | Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks |
| title_fullStr | Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks |
| title_full_unstemmed | Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks |
| title_short | Vanishing viscosity limit for a one-dimensional viscous conservation law in the presence of two noninteracting shocks |
| title_sort | vanishing viscosity limit for a one dimensional viscous conservation law in the presence of two noninteracting shocks |
| topic | shock layer viscous shocks matched asymptotic expansion nonlinear stability energy estimates 35l50 35l60 35l65 35k59 35k65 |
| url | https://doi.org/10.1515/dema-2024-0080 |
| work_keys_str_mv | AT fengli vanishingviscositylimitforaonedimensionalviscousconservationlawinthepresenceoftwononinteractingshocks AT wangjing vanishingviscositylimitforaonedimensionalviscousconservationlawinthepresenceoftwononinteractingshocks |