Branching process representation for nonlinear first-order conservation PDEs in 1D

Fuente: arXiv
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Main Authors: Hoogendijk, Jochem, Kryven, Ivan
Format: Preprint
Published: 2023
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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