Two-dimensional riemann problems: transonic shock waves and free boundary problems
We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional (2-D) Riemann problems invo...
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| Médium: | Journal article |
| Jazyk: | English |
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Springer
2022
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| _version_ | 1826311741127000064 |
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| author | Chen, G-QG |
| author_facet | Chen, G-QG |
| author_sort | Chen, G-QG |
| collection | OXFORD |
| description | We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional (2-D) Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations. |
| first_indexed | 2024-03-07T08:15:44Z |
| format | Journal article |
| id | oxford-uuid:7e91c31f-6c02-45c3-b4dc-769acd54e5b3 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:15:44Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:7e91c31f-6c02-45c3-b4dc-769acd54e5b32024-01-03T09:35:32ZTwo-dimensional riemann problems: transonic shock waves and free boundary problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7e91c31f-6c02-45c3-b4dc-769acd54e5b3EnglishSymplectic ElementsSpringer2022Chen, G-QGWe are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on their global configurations and structures. We present some recent developments in the rigorous analysis of two-dimensional (2-D) Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations. In particular, we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations. |
| spellingShingle | Chen, G-QG Two-dimensional riemann problems: transonic shock waves and free boundary problems |
| title | Two-dimensional riemann problems: transonic shock waves and free boundary problems |
| title_full | Two-dimensional riemann problems: transonic shock waves and free boundary problems |
| title_fullStr | Two-dimensional riemann problems: transonic shock waves and free boundary problems |
| title_full_unstemmed | Two-dimensional riemann problems: transonic shock waves and free boundary problems |
| title_short | Two-dimensional riemann problems: transonic shock waves and free boundary problems |
| title_sort | two dimensional riemann problems transonic shock waves and free boundary problems |
| work_keys_str_mv | AT chengqg twodimensionalriemannproblemstransonicshockwavesandfreeboundaryproblems |