Branching process representation for nonlinear first-order conservation PDEs in 1D
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910757448318976 |
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| author | Hoogendijk, Jochem Kryven, Ivan |
| author_facet | Hoogendijk, Jochem Kryven, Ivan |
| contents | We show that a large class of 1D first-order conservation PDEs can be probabilistically represented using multi-type branching processes. The representation holds when the initial conditions are linear combinations of negative exponentials. We also show that in some cases, the time of gradient blow up can be identified by studying criticality conditions of the corresponding branching processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11338 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Branching process representation for nonlinear first-order conservation PDEs in 1D Hoogendijk, Jochem Kryven, Ivan Analysis of PDEs Probability 35F20 (Primary) 35F25, 35Q35, 35Q82, 60J80, 60J85 (Secondary) We show that a large class of 1D first-order conservation PDEs can be probabilistically represented using multi-type branching processes. The representation holds when the initial conditions are linear combinations of negative exponentials. We also show that in some cases, the time of gradient blow up can be identified by studying criticality conditions of the corresponding branching processes. |
| title | Branching process representation for nonlinear first-order conservation PDEs in 1D |
| topic | Analysis of PDEs Probability 35F20 (Primary) 35F25, 35Q35, 35Q82, 60J80, 60J85 (Secondary) |
| url | https://arxiv.org/abs/2310.11338 |