相关论文: Noncommutative Burgers Equation

This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution is shown by using a Galerkin approximation, Prokhorov's…

The Lax equivalence theorem guarantees convergence of stable and consistent discretizations for linear hyperbolic partial differential equations (PDEs). For nonlinear problems, however, stability and consistency alone do not generally…

We consider Burgers equation with transverse viscosity $$\partial_tu+u\partial_xu-\partial_{yy}u=0, \ \ (x,y)\in \mathbb R^2, \ \ u:[0,T)\times \mathbb R^2\rightarrow \mathbb R.$$ We construct and describe precisely a family of solutions…

We make use of the method of modulus of continuity \cite{K-N-S} and Fourier localization technique \cite{A-H} to prove the global well-posedness of the critical Burgers equation $\partial_{t}u+u\partial_{x}u+\Lambda u=0$ in critical Besov…

In this paper, we show uniqueness and stability for the piecewise-smooth solutions to the Burgers--Hilbert equation constructed in Bressan and Zhang [Commun. Math. Sci., 15(1):165--184, 2017]. The Burgers--Hilbert equation is…

A time-dependent Hermite-Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection-diffusion equations in the unbounded domains. The time-dependent scaling factor and translating factor are introduced in…

The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian…

We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that…

The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…

The present work deals with the global solvability as well as absolute continuity of the law of the solution to stochastic generalized Burgers-Huxley (SGBH) equation driven by multiplicative space-time white noise in a bounded interval of…

Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for GL(1,R) connections with noncommutative differential calculi. The Burgers equation is formulated in this way and the Cole-Hopf transformation for…

We introduce what we call the second-order Boltzmann-Gibbs principle, which allows to replace local functionals of a conservative, one-dimensional stochastic process by a possibly nonlinear function of the conserved quantity. This…

We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…

In this paper we study a convection-diffusion equation on a star-shaped graph composed by $n$ incoming edges and $m$ outgoing edges with a nonlinearity $f\in C^1(\rr)$ satisfying some additional general conditions. First, we prove the…

The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two…

We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: $$\partial u/\partial t+(f(u))_x +\nu \Lambda^{\alpha} u= 0, t \geq 0,\ \mathbb{x} \in \mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d.$$ Here $f$ is…

Using modified Riemann-Liouville derivative, the Exp function and Exponential rational function methods are implemented to solve the time-fractional generalized Burgers-Fisher equation (TF-GBF). The TF-GBF is transformed into a nonlinear…

We discuss the mode spectrum in both the deterministic and noisy Burgers equations in one dimension. Similar to recent investigations of vortex depinning in superconductors, the spectrum is given by a non-Hermitian eigenvalue problem which…

The perturbed Burgers and KdV equations are considered. Often, the perturbation excites waves that are different from the solution one is seeking. In the case of the Burgers equation, the spontaneously generated wave is also a solution of…

In the context of adjoint-based optimization, nonlinear conservation laws pose significant problems regarding the existence and uniqueness of both direct and adjoint solutions, as well as the well-posedness of the problem for sensitivity…