Related papers: Burgers equation in the adhesion model
We review the formulation of the stochastic Burgers equation as a martingale problem. One way of understanding the difficulty in making sense of the equation is to note that it is a stochastic PDE with distributional drift, so we first…
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…
We study the stochastic Burgers equation driven by an additive Hermite sheet of order $q \ge 1$. The equation is formulated in the mild sense using the heat semigroup, and existence and uniqueness of solutions are established via a…
In this paper we prove the convergence to the stochastic Burgers equation from one-dimensional interacting particle systems, whose dynamics allow the degeneracy of the jump rates. To this aim, we provide a new proof of the second order…
We consider an evolution equation generalising the viscous Burgers equation supplemented by an initial condition which is a homogeneous random field. We develop a non-linear framework enabling us to show the existence and regularity of…
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 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.…
Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is…
In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine-Hugoniot condition that…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
In this work, we consider the stochastic Burgers-Huxley equation perturbed by multiplicative Gaussian noise, and discuss about the global solvability results and asymptotic behavior of solutions. We show the existence of a global strong…
A new three-dimensional (3D) equation is proposed, which is formed like Burgers' equation by starting with the 3D incompressible Navier-Stokes equations (NSE) and eliminating the pressure and the divergence-free constraint, but instead the…
We consider a multidimensional Burgers equation on the torus $\mathbb{T}^d$ and the whole space $\Rd$. We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we also provide estimates on…
For solutions of (inviscid, forceless, one dimensional) Burgers equation with random initial condition, it is heuristically shown that a stationary Feller-Markov property (with respect to the space variable) at some time is conserved at…
The mass transport by a Burgers velocity field is investigated in the framework of the theory of stochastic processes. Much attention is devoted to the limit of vanishing viscosity (inviscid limit) describing the "adhesion model" for the…
This work is a review with proofs of a group of results on the stochastic Burgers equation with small viscosity, obtained during the last two decades. These results jointly show that the equation makes a surprisingly good model of…
The present work demonstrates the connections between the Burgers, diffusion, and Schroedinger's equations. The starting point is a formulation of the stochastic mechanics, which is modeled along the lines of the scale relativity theory.…
We derive the statistical properties of one-dimensional Burgers dynamics with stochastic initial conditions for the velocity potential defined by a Poisson point process whose intensity follows a power law with exponent $\alpha > -1$.…
Burgers equation is one of the simplest nonlinear partial differential equations-it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a…
In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…