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.

We define the Burgers superprocess to be the solution of the stochastic partial differential equation ∂ ∂t u(t, x) =∆u(t, x) − λu(t, x)∇u(t, x) + γ √ u(t, x) W (dt, dx), where t ≥ 0, x ∈ R, and W is space-time white noise. Taking γ = 0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking λ = 0 gives the super Brownian motion, an important, measure ...

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 most general second order irrotational vector field evolution equation is constructed, that can be transformed to a single equation for the Cole–Hopf potential. The exact solution to the radial Burgers equation, with constant mass influx through a spherical supply surface, is constructed. The complex linear Schrödinger equation is equivalent to an integrable system of two coupled real vecto...

The main objective of this article is to analyse the dynamics of Burgers equation on the unit interval, driven by affine linear white noise. It is shown that the solution field of the stochastic Burgers equation generates a smooth perfect and locally compacting cocycle on the energy space L2([0, 1],R). Using multiplicative ergodic theory techniques, we establish the existence of a discrete non-...

in this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation.this method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $b(n,1)$ and $b(-n,1)$ of burgers equation and c...

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...

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...

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...

where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burger...