In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable. Keywords—Generalized Rosenau-B...

Earlier results for distributed and boundary controls of the viscous Burgers' equation were established by Burns et al. and Byrnes et al.. In their results there are technical restrictions on the sizes of the initial data. In this paper we relax these restrictions, as well as treat the Burgers' equation with other nonlinear boundary conditions.

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at rates p and I p (here p > 1/2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers' equation; the latter has shock solutions with a discontinuous jump from left density p_ ...

In this article, we prove that the Kolmogorov operator associated to the Burgers equation driven by a space-time white noise is m-dissipative. This implies several properties on the Kolmogorov equation. This result is obtained thanks to the introduction of a modified Kolmogorov operator. New a priori estimates on the solutions of the Burgers equation and on the invariant measure are obtained. T...

The Burgers’ equation is an important and basic nonlinear partial differential equation in fluid dynamics, and has been used as a model equation in other fields, such as modeling of shock waves, gas dynamics, turbulence, and large bubble structures consisting of clusters of galaxies in space. Many researchers have proposed various numerical methods for solving the Burgers’ equation, such as the...

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed. Burgers equation [1],...

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 ...

We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in L for p > d. In the case of torus we also establish a uniform in ν a priori estimate and consider a limit ν ↘ 0 for potential solutions. In the case of R uniform with respect to ν a priori estimate...

We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut = νuxx − uux + u+ h(x), 0 < x < 2π, t > 0, u(0, t) = u(2π, t), u(x,0) = u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a steady state solution and global stabil...

This paper introduces an anisotropic diffusion oscillation reduction (ADOR) scheme for shock wave computations. The connection is made between digital image processing, in particular, image edge detection, and numerical shock capturing. Indeed, numerical shock capturing can be formulated on the lines of iterative digital edge detection. Various anisotropic diffusion and super diffusion operator...