2014/06/22 by Yuri Bakhtin, Bakhtin, Yuri
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #35R60 #37H99 #37L40 #37L55 #60G55 #60K35 #Analysis of PDEs (math.AP) #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1406.5660
openalex publication_date 2014/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on the study of one-sided minimizers of the relevant action is different. In contrast with previous work, finite time coalescence of the minimizers does not hold, and hyperbolicity (exponential convergence of minimizers in reverse time) is not known. In order to establish a One Force --- One Solution principle on each ergodic component, we use an extremely soft method to prove a weakened hyperbolicity property and to construct Busemann functions along appropriate subsequences.