Branching process representation for Burgers-like nonlinear partial differential equations

Autor:	Hoogendijk, Jochem, Kryven, Ivan
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Probability 35F20 (Primary) 35F25 35Q35 35Q82 60J80 60J85 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We show that a large class of 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. This class contains Burgers' equation in 1D, which may develop a gradient blow-up in finite time, as well as other equations with more general nonlinearities. We also show how the time of gradient blow up can be identified by studying criticality conditions of the corresponding branching processes.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.11338 Zobrazit plný text záznamu View this record from Arxiv