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Inviscid Burgers equation with random kick forcing in noncompact setting. (English) Zbl 1338.37117
Summary: 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.

MSC:
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
37L55 Infinite-dimensional random dynamical systems; stochastic equations
35R60 PDEs with randomness, stochastic partial differential equations
37H10 Generation, random and stochastic difference and differential equations
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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