相关论文: Noise-Induced Stabilization of Planar Flows I
We consider the stochastic nonlinear Schr\"odinger equation driven by linear multiplicative noise in the mass-supercritical case. Given arbitrary $K$ solitary waves with distinct speeds, we construct stochastic multi-solitons pathwisely in…
This work investigates the boundary stabilization of flows in star-shaped and tree-shaped networks of open channels governed by the Saint-Venant equations with a friction term. Due to the existence of the friction term, the steady-states…
Modern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are implemented to tackle highly irregular problems where…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in $L^2$-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
In this paper, the stabilization problem with closed-loop domain of attraction (DOA) enlargement for discrete-time general nonlinear plants is solved. First, a sufficient condition for asymptotic stabilization and estimation of the…
This work aims to investigate the well-posedness and the existence of ergodic invariant measures for a class of third grade fluid equations in bounded domain $D\subset\mathbb{R}^d,d=2,3,$ in the presence of a multiplicative noise. First, we…
We consider in this paper some class of perturbation for the semilinear wave equation with critical (in the conformal transform sense) power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium…
This paper proposes and analyzes a novel fully discrete finite element scheme with the interpolation operator for stochastic Cahn-Hilliard equations with functional-type noise. The nonlinear term satisfies a one-side Lipschitz condition and…
We extend our recently introduced stochastic nonlocal traffic flow model to more general random perturbations, including Markovian noise derived from a discretized Jacobi-type stochastic differential equation. Invoking a deterministic…
This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we…
This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency…
We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
We study numerically the integrable turbulence in the framework of the focusing one-dimensional nonlinear Schrodinger equation using a new method -- the "growing of turbulence". We add to the equation a weak controlled pumping term and…
This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to…
Nonlinear dispersive partial differential equations such as the nonlinear Schr\"odinger equations can have solutions that blow-up. We numerically study the long time behavior and potential blowup of solutions to the focusing…