Martingale and Weak Solutions for a Stochastic Nonlocal Burgers Equation on Bounded Intervals

2014/10/28 by Guangying Lv, Lv, Guangying, Jinqiao Duan +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.PR #msc:35K20 #msc:60H15 #msc:60H40

paper · pdf · doi:10.48550/arxiv.1410.7691

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arxiv created 2014/10/28 · arxiv updated 2014/10/29

Abstract

This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's theorem and Skorokhod's embedding theorem. The same Galerkin approximation also leads to the existence of weak solution for the corresponding deterministic nonlocal Burgers equation on a bounded domain.

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