48 citations · 255 across the 27 of their papers we have counts for
19 papers · 1 filter
Exponential stability of the flow for a generalised Burgers equation on a circle
Ana Djurdjevac, Armen Shirikyan
The paper deals with the problem of stability for the flow of the 1D Burgers equation on a circle. Using some ideas from the theory of positivity preserving semigroups, we establis…
Stabilisation of a viscous conservation law by a one-dimensional external force
Ana Djurdjevac, Armen Shirikyan
We study a damped scalar conservation law driven by the sum of a fixed external force and a localised one-dimensional control. The problem is considered in a bounded domain and is…
Rayleigh-Bénard convection with stochastic forcing localised near the bottom
Juraj Földes, Armen Shirikyan
We prove stochastic stability of the three-dimensional Rayleigh-Bénard convection in the infinite Prandtl number regime for any pair of temperatures maintained on the top and the b…
Mixing via controllability for randomly forced nonlinear dissipative PDEs
Sergei Kuksin, Vahagn Nersesyan, Armen Shirikyan
We continue our study of the problem of mixing for a class of PDEs with very degenerate noise. As we established earlier, the uniqueness of stationary measure and its exponential s…
Controllability implies mixing II. Convergence in the dual-Lipschitz metric
Armen Shirikyan
This paper continues our study of the interconnection between controllability and mixing properties of random dynamical systems. We begin with an abstract result showing that the a…
Exponential mixing for a class of dissipative PDEs with bounded degenerate noise
Sergei Kuksin, Vahagn Nersesyan, Armen Shirikyan
We study a class of discrete-time random dynamical systems with compact phase space. Assuming that the deterministic counterpart of the system in question possesses a dissipation p…