Related papers: Exponential Decay for dispersion managed solitons …
For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of the density from which we derive some explicit Gaussian…
We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of…
Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the…
We consider the Boltzmann equation in convex domain with non-isothermal boundary of diffuse reflection. For both unsteady/steady problems, we construct solutions belong to $W^{1,p}_x$ for any $p<3$. We prove that the unsteady solution…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
Dissipative solitons are localized solutions in non-integrable and non-conservative nonlinear system, due to a balance of nonlinearity, dispersion, filtering, and loss/gain. Different from conventional soliton, they exhibit extremely…
We perform a Gabor analysis for a large class of evolution equations with constant coefficients. We show that the corresponding propagators have a very sparse Gabor matrix, displaying off-diagonal exponential decay. The results apply to…
In this article we prove the existence and uniqueness for degenerate stochastic differential equations with Sobolev (possibly singular) drift and diffusion coefficients in a generalized sense. In particular, our result covers the classical…
In the present paper we discuss problems concerning evolutions of densities related to Ito diffusions in the framework of the statistical exponential manifold. We develop a rigorous approach to the problem, and we particularize it to the…
We develop a geometric and analytic framework for polynomial partial differential equations posed on thin annuli in the plane. Using renormalized Sobolev inner products, we construct Sobolev orthogonal polynomial bases adapted to the thin…
The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction…
Dissipative solitons are non-decaying out-of-equilibrium entities that result from double balances between gain and loss, as well as nonlinearity and dispersion. Here we describe a scenario where double balances rely on the presence of…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
We study the dynamics of localized pulses in the complex cubic-quintic Ginzburg-Landau (GL) equation with strong nonlinearity management. The generalized complex GL equation, averaged over rapid modulations of the nonlinearity, is derived.…
We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a…
We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of…
This paper is concerned with controllability and stabilization properties of the dispersion generalized Benjamin equation on the periodic domain $\mathbb{T}.$ First, by assuming the control input acts on all the domain, the system is proved…
Considering the existence of nonconformal stochastic fluctuations in the metric tensor a generalized uncertainty principle and a deformed dispersion relation (associated to the propagation of photons) are deduced. Matching our model with…
We establish exponential decay of correlations of all orders for locally $G$-accessible isometric extensions of transitive Anosov flows, under the assumption that the strong stable and strong unstable foliations of the base Anosov flow are…
We establish weak well-posedness for SDEs having discontinuous diffusion coefficients and general distributional drifts that may introduce local blow up effects. Our drifts satisfy minimal assumptions, i.e.\,we assume only that the Cauchy…