相关论文: Functional sensitivity of Burgers and related equa…
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…
The well-known analytical solution of Burgers' equation is extended to curvilinear coordinate systems in three-dimensions by a method which is much simpler and more suitable to practical applications than that previously used. The results…
We present a study of the Burgers equation in one and two dimensions $d=1,2$ following the analytic approach indicated in the previous paper I. For the problem of the initial conditions decay we consider two classes of initial condition…
We consider a nonhomogeneous Burgers equation with time variable coefficients, and obtain an explicit solution of the general initial value problem in terms of solution to a corresponding linear ODE. Special exact solutions such as…
The randomly driven Burgers equation with pressure is considered as a 1D model of strong turbulence of compressible fluid. It is shown that infinitely small pressure provides a finite effect on the velocity and density statistics and this…
The last decades witnessed a renewal of interest in the Burgers equation. Much activities focused on extensions of the original one-dimensional pressureless model introduced in the thirties by the Dutch scientist J.M. Burgers, and more…
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…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
Burgers equation is one of the simplest nonlinear partial differential equations-it combines the basic processes of diffusion and nonlinear steepening. In some applications it is appropriate for the diffusion coefficient to be a…
We investigate the stability of large-scale structures in Burgers' equation under the perturbation of high wave-number noise in the initial conditions. Analytical estimates are obtained for random initial data with spatial spectral density…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
We consider an evolution equation generalising the viscous Burgers equation supplemented by an initial condition which is a homogeneous random field. We develop a non-linear framework enabling us to show the existence and regularity of…
This paper is an introduction to the theory of 1d stochastic Burgers equation under periodic boundary conditions and with a stochastic force, sufficiently smooth in the space variable. We prove the classical results on the existence and…
Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the…
We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the $L^2$-based Sobolev spaces. We introduce appropriate time weighted spaces to derive…
In this work we consider the problem of constructing initial conditions for a flow model such that the resulting flow evolution leads to a self-similar energy cascade consistent with Kolmogorov's statistical theory of turbulence. As a first…
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…
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers'…
The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in…
We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a…