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.

Intermittency effects in Burgers equation driven by thermal noise. Abstract For the Burgers equation driven by thermal noise leading asymp-totics of pair and high-order correlators of the velocity field are found for finite times and large distances. It is shown that the intermittency takes place: some correlators are much larger than their reducible parts. Intermittency implies strong non-Gaus...

Abstract We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, temporal part is discretized by finite difference method together with ? -weighted scheme. Then, approximation of spatial unknown function and its derivatives, we use mixed approach based on Lucas Fibonacci polynomials. With help these ap...

Optimal control problems (OCP) for Burgers equation are important for the development of numerical methods for optimal control of more complicated models in fluid dynamics such as Navier-Stokes equations. In this work, we analyze variant preconditioners for the saddle point problem arising from boundary control of unsteady Burgers equation. As for a solution approach for the discretization of t...

A stochastic representation of the dynamics of the Burger's turbulence model and of the two{dimensional turbulence is developed. The random velocity eld is regarded as a multivariate stochastic Markov process deened by a master equation. It is shown that Burgers' equation and the two{dimensional Navier{Stokes equation are obtained as the macroscopic equations for the averages of the underlying ...

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions complex plane, concentrating dynamics of singularities their relationship solution real line. For an initial condition simple pole each upper- lower-half planes, apply formal as...