Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations
A compactness framework is established for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing ways to employ these new properti...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2003
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| _version_ | 1797063336498561024 |
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| author | Chen, G Li, B Li, T |
| author_facet | Chen, G Li, B Li, T |
| author_sort | Chen, G |
| collection | OXFORD |
| description | A compactness framework is established for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing ways to employ these new properties in the method of compensated compactness. Then this framework is applied to establish the existence, compactness, and decay of entropy solutions in L ∞ for the Euler equations in nonlinear elastodynamics with a more general stress-strain relation than those for the previous existence results. This compactness framework is further applied to solving the Euler equations of conservation laws of mass, momentum, and energy for a class of thermoelastic media, and the equations of motion of viscoelastic media with memory. |
| first_indexed | 2024-03-06T20:58:22Z |
| format | Journal article |
| id | oxford-uuid:3a087011-ca1d-4d54-8b39-2834748400ce |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:58:22Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:3a087011-ca1d-4d54-8b39-2834748400ce2022-03-26T13:59:07ZEntropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related EquationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3a087011-ca1d-4d54-8b39-2834748400ceEnglishSymplectic Elements at Oxford2003Chen, GLi, BLi, TA compactness framework is established for approximate solutions to the Euler equations in one-dimensional nonlinear elastodynamics by identifying new properties of the Lax entropies, especially the higher order terms in the Lax entropy expansions, and by developing ways to employ these new properties in the method of compensated compactness. Then this framework is applied to establish the existence, compactness, and decay of entropy solutions in L ∞ for the Euler equations in nonlinear elastodynamics with a more general stress-strain relation than those for the previous existence results. This compactness framework is further applied to solving the Euler equations of conservation laws of mass, momentum, and energy for a class of thermoelastic media, and the equations of motion of viscoelastic media with memory. |
| spellingShingle | Chen, G Li, B Li, T Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations |
| title | Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations |
| title_full | Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations |
| title_fullStr | Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations |
| title_full_unstemmed | Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations |
| title_short | Entropy Solutions in L ∞ for the Euler Equations in Nonlinear Elastodynamics and Related Equations |
| title_sort | entropy solutions in l ∞ for the euler equations in nonlinear elastodynamics and related equations |
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