Convergence of a continuous BGK model for initial boundary-value problems for conservation laws
We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK) model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy i...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2001-11-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2001/72/abstr.html |
| _version_ | 1818772008395079680 |
|---|---|
| author | Driss Seghir |
| author_facet | Driss Seghir |
| author_sort | Driss Seghir |
| collection | DOAJ |
| description | We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK) model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem's data. As an application, we establish the hydrodynamic limit for a $2imes2$ relaxation system with general data. Also we construct a new family of convergent continuous BGK models with simple maxwellians different from the $chi$ models. |
| first_indexed | 2024-12-18T10:02:31Z |
| format | Article |
| id | doaj.art-0851b3a14fa44746aac9a98dc964cdef |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T10:02:31Z |
| publishDate | 2001-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-0851b3a14fa44746aac9a98dc964cdef2022-12-21T21:11:37ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912001-11-01200172118Convergence of a continuous BGK model for initial boundary-value problems for conservation lawsDriss SeghirWe consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK) model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem's data. As an application, we establish the hydrodynamic limit for a $2imes2$ relaxation system with general data. Also we construct a new family of convergent continuous BGK models with simple maxwellians different from the $chi$ models.http://ejde.math.txstate.edu/Volumes/2001/72/abstr.htmlConservation lawsboundary conditionBGK model. |
| spellingShingle | Driss Seghir Convergence of a continuous BGK model for initial boundary-value problems for conservation laws Electronic Journal of Differential Equations Conservation laws boundary condition BGK model. |
| title | Convergence of a continuous BGK model for initial boundary-value problems for conservation laws |
| title_full | Convergence of a continuous BGK model for initial boundary-value problems for conservation laws |
| title_fullStr | Convergence of a continuous BGK model for initial boundary-value problems for conservation laws |
| title_full_unstemmed | Convergence of a continuous BGK model for initial boundary-value problems for conservation laws |
| title_short | Convergence of a continuous BGK model for initial boundary-value problems for conservation laws |
| title_sort | convergence of a continuous bgk model for initial boundary value problems for conservation laws |
| topic | Conservation laws boundary condition BGK model. |
| url | http://ejde.math.txstate.edu/Volumes/2001/72/abstr.html |
| work_keys_str_mv | AT drissseghir convergenceofacontinuousbgkmodelforinitialboundaryvalueproblemsforconservationlaws |