This document provides a proof that the solutions to Convectively Filtered Burgers equation, will converge to the entropy solution of Inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of Inviscid Burgers equation. That solution is then shown to be the entropy solution.

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

Scaling limits for the solution of Burgers equation are investigated. It is shown that the limiting distribution for the solution of Wick type Burgers equation with Gaussian initial data is the same as that for the solution of Burgers equation with ordinary product calculated in LPW96].

The paper is concerned with a numerical simulation of Burgers flow as a simplified model of unsteady flow of a compressible viscous fluid. Viscous Burgers equation represents many of the properties of unsteady compressible NavierStokes equations, such as nonlinear convection and viscous diffusion leading to shock waves and boundary layers. A one-dimensional Burgers equation is frequently used t...

We propose a new approach for the analysis of stationary correlation functions of 1D Burgers equation driven by a random force. We use this to study the asymptotic behavior of the probability distribution of velocity gradients and velocity increments. PACS number 47.27.Gs, 03.40.Gc Statistical properties of solutions of random forced Burgers equation have been a subject of intensive studies rec...

The coupled viscous Burgers’ equation which was derived by Esipov in 1995 to study the model of poly-dispersive sedimentation. The system of coupled viscous Burgers’ equation is a simple model of sedimentation or evolution of scaled volume concentrations of two kinds of particles in fluid suspensions or colloids under the effect of gravity. Coupled Burgers’ equation can be written in the follow...

In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation ut + (−∂ 2 x) α/2u+ uux = 0 with α ∈ (1, 2) is studied. It is shown that if the nondecreasing initial datum approaches the constant states u± (u− < u+) as x → ±∞, respectively, then the corresponding solution converges toward the rarefaction wave, i.e. the unique entropy sol...

In this paper we study the generalized Burgers equation ut + (u /2)x = f(t)uxx, where f(t) > 0 for t > 0 . We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to L∞(R), as well it is obtained the decay rates of u in L norm are algebra order for p ∈ [1,∞[.

A continuum limit of the non-Hermitian spin-1/2 chain, conjectured recently to belong to the universality class of the noisy Burgers or, equivalently, Kardar-Parisi-Zhang equation, is obtained and analyzed. The Galilean in-variance of the Burgers equation is explicitly realized in the operator algebra. In the quasi-classical limit we nd nonlinear soliton excitations exhibiting the ! / k z dispe...

This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so by first establishing convergence to a weak solution of the inviscid Burgers equation and then showing that the weak solution is the entropy solution. Then t...