ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
We are concerned with entropy solutions u in L∞ of nonlinear hyperbolic systems of conservation laws. It is shown that, given any entropy function η and any hyperplane t = const:, if u satisfies a vanishing mean oscillation property on the half balls, then η(u) has a trace H d-almost everywhere on t...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826270191124742144 |
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| author | Chen, G Torres, M |
| author_facet | Chen, G Torres, M |
| author_sort | Chen, G |
| collection | OXFORD |
| description | We are concerned with entropy solutions u in L∞ of nonlinear hyperbolic systems of conservation laws. It is shown that, given any entropy function η and any hyperplane t = const:, if u satisfies a vanishing mean oscillation property on the half balls, then η(u) has a trace H d-almost everywhere on the hyperplane. For the general case, given any set E of finite perimeter and its inner unit normal ν : ∂*E → Sd and assuming the vanishing mean oscillation property of u on the half balls, we show that the weak trace of the vector field (η(u); q(u)), defined in Chen-Torres-Ziemer [9], satisfies a stronger property for any entropy pair (η q). We then introduce an approach to analyze the structure of bounded entropy solutions for the isentropic Euler equations. |
| first_indexed | 2024-03-06T21:36:58Z |
| format | Journal article |
| id | oxford-uuid:46977f41-8f6a-41a8-b2d5-6d0176bb6b0e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:36:58Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:46977f41-8f6a-41a8-b2d5-6d0176bb6b0e2022-03-26T15:14:34ZON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWSJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:46977f41-8f6a-41a8-b2d5-6d0176bb6b0eEnglishSymplectic Elements at Oxford2011Chen, GTorres, MWe are concerned with entropy solutions u in L∞ of nonlinear hyperbolic systems of conservation laws. It is shown that, given any entropy function η and any hyperplane t = const:, if u satisfies a vanishing mean oscillation property on the half balls, then η(u) has a trace H d-almost everywhere on the hyperplane. For the general case, given any set E of finite perimeter and its inner unit normal ν : ∂*E → Sd and assuming the vanishing mean oscillation property of u on the half balls, we show that the weak trace of the vector field (η(u); q(u)), defined in Chen-Torres-Ziemer [9], satisfies a stronger property for any entropy pair (η q). We then introduce an approach to analyze the structure of bounded entropy solutions for the isentropic Euler equations. |
| spellingShingle | Chen, G Torres, M ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS |
| title | ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS |
| title_full | ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS |
| title_fullStr | ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS |
| title_full_unstemmed | ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS |
| title_short | ON THE STRUCTURE OF SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS |
| title_sort | on the structure of solutions of nonlinear hyperbolic systems of conservation laws |
| work_keys_str_mv | AT cheng onthestructureofsolutionsofnonlinearhyperbolicsystemsofconservationlaws AT torresm onthestructureofsolutionsofnonlinearhyperbolicsystemsofconservationlaws |