Initial Boundary Value Problem For A Non-conservative System In Elastodynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911991428284416 |
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| author | Joseph, Kayyunnapara Divya Dinesh, P. A |
| author_facet | Joseph, Kayyunnapara Divya Dinesh, P. A |
| contents | This paper is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain $x > 0, t > 0$. The number of boundary conditions to be prescribed at the boundary $x = 0$, depend on the number of characteristics entering the domain. Since our system is nonlinear the characteristic speeds depends on the unknown and the direction of the characteristics curves are known apriori. As it is well known, the boundary condition has to be understood in a generalised way. One of the standard way is using vanishing viscosity method. We use this method to construct solution for a particular class of initial and boundary data, namely the initial and boundary datas that lie on the level sets of one of the Riemann invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Initial Boundary Value Problem For A Non-conservative System In Elastodynamics Joseph, Kayyunnapara Divya Dinesh, P. A Analysis of PDEs 35A20, 35L50, 35R05 This paper is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain $x > 0, t > 0$. The number of boundary conditions to be prescribed at the boundary $x = 0$, depend on the number of characteristics entering the domain. Since our system is nonlinear the characteristic speeds depends on the unknown and the direction of the characteristics curves are known apriori. As it is well known, the boundary condition has to be understood in a generalised way. One of the standard way is using vanishing viscosity method. We use this method to construct solution for a particular class of initial and boundary data, namely the initial and boundary datas that lie on the level sets of one of the Riemann invariants. |
| title | Initial Boundary Value Problem For A Non-conservative System In Elastodynamics |
| topic | Analysis of PDEs 35A20, 35L50, 35R05 |
| url | https://arxiv.org/abs/2408.08748 |