The Burgers equation with Poisson random forcing

On the Burgers-poisson Equation

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

Optimal Control of Stochastic Burgers’ Equation with Random Forcing Using Weiner Chaos Expansion

Introduction . Control of nonlinear stochastic partial differential equations (SPDEs) has acquired significant attention in recent years. But due to the nonlinearity and randomness of the system, such problem is very challenging and difficult to handle. A typical example in this field is the control of stochastic Burgers’ equations (SBEs) with random forcing, which is presented in [2] as a step...

Burgers Equation with Random Boundary Conditions

We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.

Group Invariant Solutions of Burgers-Poisson Equation

In this paper, a nonlinear dispersive wave equation Burgers-Poisson (BP) equation is considered. We present a classification of group invariant solutions for the BP equation by using classical Lie method. Mathematics Subject Classification; 35Q53

Invariant measures for Burgers equation with stochastic forcing