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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.00116 |
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| _version_ | 1866929625976799232 |
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| author | Ancona, Fabio Talamini, Luca |
| author_facet | Ancona, Fabio Talamini, Luca |
| contents | Consider a scalar conservation law with a spatially discontinuous flux at a single point x=0, and assume that the flux is uniformly convex when x\neq 0. Given an interface connection (A,B), we define a backward solution operator consistent with the concept of AB-entropy solution [4,13,16]. We then analyze the family A^{[AB]}(T) of profiles that can be attained at time T>0 by AB-entropy solutions with L^\infty-initial data. We provide a characterization of A^{[AB]}(T) as fixed points of the backward-forward solution operator. As an intermediate step we establish a full characterization of A^{[AB]}(T) in terms of unilateral constraints and Ole\vınik-type estimates, valid for all connections. Building on such a characterization we derive uniform BV bounds on the flux of AB-entropy solutions, which in turn yield the L^1_{loc}-Lipschitz continuity in time of these solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00116 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Backward-forward characterization of attainable set for conservation laws with spatially discontinuous flux Ancona, Fabio Talamini, Luca Analysis of PDEs Consider a scalar conservation law with a spatially discontinuous flux at a single point x=0, and assume that the flux is uniformly convex when x\neq 0. Given an interface connection (A,B), we define a backward solution operator consistent with the concept of AB-entropy solution [4,13,16]. We then analyze the family A^{[AB]}(T) of profiles that can be attained at time T>0 by AB-entropy solutions with L^\infty-initial data. We provide a characterization of A^{[AB]}(T) as fixed points of the backward-forward solution operator. As an intermediate step we establish a full characterization of A^{[AB]}(T) in terms of unilateral constraints and Ole\vınik-type estimates, valid for all connections. Building on such a characterization we derive uniform BV bounds on the flux of AB-entropy solutions, which in turn yield the L^1_{loc}-Lipschitz continuity in time of these solutions. |
| title | Backward-forward characterization of attainable set for conservation laws with spatially discontinuous flux |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.00116 |