相关论文: The Burgers equation as electrohydrodynamic model …

We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global…

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution…

We prove the existence and uniqueness of a classical solution to a multidimensional non-potential stochastic Burgers equation with H\"older continuous initial data. Our motivation is the adhesion model in the theory of formation of the…

When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets…

We consider one-dimensional exclusion processes with long jumps given by a transition probability of the form $p_n(\cdot)=s(\cdot)+\gamma_na(\cdot)$, such that its symmetric part $s(\cdot)$ is irreducible with finite variance and its…

Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the…

We prove that the Burgers flow with a steady external forcing has a unique steady state which is a sink. Although this flow cannot be linearized through Cole-Hopf transforms, we prove that it has a convergent Koopman Modes decomposition.…

We describe the asymptotic behaviour of solutions of unviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the…

We prove the existence and uniqueness of positive analytical solutions with positive initial data to the mean field equation (the Dyson equation) of the Dyson Brownian motion through the complex Burgers equation with a force term on the…

We investigate the statistical properties of one-dimensional Burgers dynamics evolving from stochastic initial conditions defined by a Poisson point process for the velocity potential, with a power-law intensity. Thanks to the geometrical…

The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in…

The Moyal *-deformed noncommutative version of Burgers' equation is considered. Using the *-analog of the Cole-Hopf transformation, the linearization of the model in terms of the linear heat equation is found. Noncommutative q-deformations…

Solutions of the linearized Vlasov-Poisson equations for the electric field radiated by a time varying point charge in a three-dimensional, unbounded, spatially homogeneous plasma with a uniform background magnetic field and a uniform…

In this paper we present numerical models for electrodynamical flows with time-dependent electrical fields with transport of bubbles. Such models are applied in e-jet printing, e.g., additive manufacturing (AM), and convective cooling,…

In this article we find the solution of the Burger equation with viscosity applying the boundary layer theory. In addition, we will observe that the solution of Burger equation with viscosity converge to the solution of Burger stationary…

We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term $-\kappa^{2} x+f(t)$, $\kappa\in\mathbb{R}$. Two methods existing for the case $\kappa=0$ are adapted and generalized using…

We derive from a class of microscopic asymmetric interacting particle systems on ${\mathbb Z}$, with long range jump rates of order $|\cdot|^{-(1+\alpha)}$ for $0<\alpha<2$, different continuum fractional SPDEs. More specifically, we show…

The topic of this paper are similarity solutions occurring in multi-dimensional Burgers' equation. We present a simple derivation of the symmetries appearing in a family of generalizations of Burgers' equation in $d$-space dimensions. These…

Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic…

We explore a connection of the deterministically forced Burgers equation for local velocity fields with probabilistic solutions of the Schr\"{o}dinger boundary data problem. An issue of deducing the most likely interpolating dynamics from…