Related papers: Analytic solutions for the Burgers equation with s…
We investigate the time periodic solutions to the viscous Burgers equation $u_t -\mu u_{xx} + uu_x = f$ for irregular forcing terms. We prove that the corresponding Burgers operator is a diffeomorphism between appropriate function spaces.
In this paper we present a technique for constructing robust solvers for stiff algebraic source terms, such as those typically used for modelling relaxation processes in hyperbolic systems of partial differential equations describing…
In this paper we present iterative and noniterative splitting methods, which are used to solve stochastic Burgers' equations. The non-iterative splitting methods are based on Lie-Trotter and Strang-splitting methods, while the iterative…
In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine-Hugoniot condition that…
We investigate generalizations of the Burgers and Burgers-Huxley equations. The investigations we offer focus attention mainly on presenting explict analytical solutions by means of relating these generalized equations to relativistic 1+1…
The symmetry classification of the two dimensional Burgers equation with variable coefficient is considered. Symmetry algebra is found and a classification of its subalgebras, up to conjugacy, is obtained. Similarity reductions are…
Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random…
We present a simple analytical method to solve master equations for finite temperatures and any initial conditions, which consists in the expansion of the density operator into normal modes. These modes and the expansion coefficients are…
We prove that the viscous Burgers equation has a globally defined smooth solution in all dimensions provided the initial condition and the forcing term are smooth and bounded together with their derivatives. Such solutions may have infinite…
In this paper, we study the strong and weak convergence rates for multi-scale one-dimensional stochastic Burgers equation. Based on the techniques of Galerkin approximation, Kolmogorov equation and Poisson equation, we obtain the slow…
Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived.…
A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the Complex Burgers` Hierarchy is performed. Moreover, a detailed application of the reduction process through the…
In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and…
Reduction operators of generalized Burgers equations are studied. A connection between these equations and potential fast diffusion equations with power nonlinearity -1 via reduction operators is established. Exact solutions of generalized…
A study is presented on the convergence of the computation of coupled advection-diffusion-reaction equations. In the computation, the equations with different coefficients and even types are assigned in two subdomains, and Schwarz iteration…
We review the formulation of the stochastic Burgers equation as a martingale problem. One way of understanding the difficulty in making sense of the equation is to note that it is a stochastic PDE with distributional drift, so we first…
Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the…
We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.
We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a modified energy method to prove the existence of small, smooth solutions over…
We introduce a new concepts of weak solution for the conservative stochastic Burgers equation in any dimension. The definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not…