Related papers: Mixing via controllability for randomly forced non…

In the paper we study a measure version of the evolutionary nonlinear Boltzmann-type equation in which we admit a random number of collisions of particles. We consider first a stationary model and use two methods to find its fixed points:…

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…

We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…

This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular nonlinearities and measure data extending the works of…

In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

In this note we review recent progress in the problem of mixing for a nonlinear PDE of parabolic type, perturbed by a bounded random force.

This paper investigates robust synchronization for multi-agent systems (MASs) governed by parabolic partial differential equations in the presence of both observable and unobservable disturbances. Using only boundary output measurements, a…

This paper examines Poisson stable (including stationary, periodic, almost periodic, Levitan almost periodic, Bohr almost automorphic, pseudo-periodic, Birkhoff recurrent, pseudo-recurrent, etc.) measures and limit theorems for stochastic…

We utilize Gaussian measure preserving systems to prove the existence and genericity of Lebesgue measure preserving transformations $T:[0,1]\rightarrow [0,1]$ which exhibit both mixing and rigidity behavior along families of asymptotically…

This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…

This paper aims to develop the stability theory for singular stochastic Markov jump systems with state-dependent noise, including both continuous- and discrete-time cases. The sufficient conditions for the existence and uniqueness of a…

We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

In this paper, we investigate the stabilization of a linear Bresse system with one singular local frictional damping acting in the longitudinal displacement, under fully Dirichlet boundary conditions. First, we prove the strong stability of…

This work considers a system coupling a viscous Burgers equation (aimed to describe a simplified model of $1D$ fluid flow) with the ODE describing the motion of a point mass moving inside the fluid. The point mass is possibly under the…

We study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix…

We show existence, uniqueness and stability for a family of stationary subsonic compressible Euler flows with mass-additions in two-dimensional rectilinear ducts, subjected to suitable time-independent multi-dimensional boundary conditions…

We propose a novel framework for stabilization, with an estimate of the region of attraction, of quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow-up phenomena when null boundary inputs are imposed.…

We modify the coupling method established in [22, 20] and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate Levy noises. In particular, these Levy noises include $\alpha$-stable noises (0 <…