2020/05/19 by Julien Berestycki, Éric Brunet-Gouet, Berestycki, Julien +5 · 4 citations
Mathematics · Economics, Econometrics and Finance · Physics and Astronomy · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2005.09384
We study a free boundary problem for a parabolic partial differential\nequation in which the solution is coupled to the moving boundary through an\nintegral constraint. The problem arises as the hydrodynamic limit of an\ninteracting particle system involving branching Brownian motion with selection,\nthe so-called Brownian bees model which is studied in a companion paper. In\nthis paper we prove existence and uniqueness of the solution to the free\nboundary problem, and we characterise the behaviour of the solution in the\nlarge time limit.\n