相关论文: On blow up NLS with a multiplicative noise

Using the maximum-likelihood detector (MLD) of a soliton with timing jitter and noise, other than walk-out of the bit interval, timing jitter does not degrade the performance of MLD. When the MLD is simulated with important sampling method,…

We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the…

Stochastic Bloch equations which model the fluorescence of two level molecules and atoms, NMR experiments and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a…

We consider the blowup rate for blowup solutions to $L^2$-critical, focusing NLS with a harmonic potential and a rotation term. Under a suitable spectral condition we prove that there holds the "$\log$-$\log$ law" when the initial data is…

We provide an example for stabilization by noise. Our approach does not rely on monotonicity arguments due to the presence of higher order differential operators or mixing properties of the system as the noise might be highly degenerate. In…

In this note we discuss the global dynamics of an integrable nonlocal NLS on $\mathbb{R}$, which has been the object of recent investigation by integrable systems methods. We prove two results which are in striking contrast with the case of…

We consider a system of interacting SDEs on the integer lattice with multiplicative noise and a drift satisfying the finite Osgood's condition. We show instantaneous everywhere blowup for initial profiles decaying slower than $\exp \left(…

We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for…

For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…

We consider the $L^2$ critical inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^N$ $$ i \partial_t u +\Delta u +|x|^{-b} |u|^{\frac{4-2b}{N}}u = 0, $$ where $N\geq 1$ and $0<b<2$. We prove that if $u_0\in…

The effect of multiplicative noise to the Turing instability of the Brusselator system is investigated. We show that when the noise acts on both of the concentrations with the same intensities, then the Turing instability is suppressed…

We study small random perturbations by additive space-time white noise of a reaction-diffusion equation with a unique stable equilibrium and solutions which blow up in finite time. We show that for initial data in the domain of attraction…

In this paper, we consider a 3d cubic focusing nonlinear Schr\"odinger equation (NLS) with slowing decaying potentials. Adopting the variational method of Ibrahim-Masmoudi-Nakanishi \cite{IMN}, we obtain a condition for scattering. It is…

In this paper we develop two different types of criteria for the finite time blow-up solutions to the combined nonlinear Schr\"odinger equation in 1D. The first one is a negative energy criterion developed for triple combined nonlinearity…

We consider a class of stochastic evolution equations that include in particular the stochastic Camassa--Holm equation. For the initial value problem on a torus, we first establish the local existence and uniqueness of pathwise solutions in…

We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…

We study the possibility of non-simultaneous blow-up for positive solutions of a coupled system of two semilinear equations, $u_t = J*u-u+ u^\alpha v^p$, $v_t =\Delta v^+u^qv^\beta$, $p, q, \alpha, \beta>0$ with homogeneous Dirichlet…

The finite time blowup in the almost sure sense of a class of space-time fractional stochastic partial differential equations is discussed. Both the cases of white noise and colored noise are considered. The sufficient and necessary…

We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds…

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…