Related papers: Instantons in Burgers Equation
This paper derives a complete analytical solution for the probability distribution of the configuration of a non-holonomic vehicle that moves in two spatial dimensions by satisfying the unicycle kinematic constraints and in presence of…
In this paper, we provide two-sided estimates and uniform asymptotics for the solution of $d$-dimensional critical fractal Burgers equation $u_t-\Delta^{\alpha/2}u+b\cdot \nabla\left(u|u|^q\right)=0$, $\alpha\in(1,2)$, $b\in\mathbb R^d$ for…
In this paper, we show that the positive multiples of a particular function $F$ -- which is singular with a jump discontinuity at the origin -- are finite-time global attractors in $L^2$ for generic odd, smooth solutions of the one…
In these notes we give a simple proof of the second-order Boltzmann-Gibbs Principle, which is the main tool in order to prove that the equilibrium fluctuations of the WASEP are given, in the regime of the critical strength asymmetry, by the…
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inviscid case. The viscous solution is written as a rational…
We prove finite time blowup of the Burgers-Hilbert equation. We construct smooth initial data with finite $H^5$-norm such that the $L^\infty$-norm of the spacial derivative of the solution blows up. The blowup is an asymptotic self-similar…
In this note, we consider some Burgers-like equations involving Laguerre derivatives and demonstrate that it is possible to construct specific exact solutions using separation of variables. We prove that a general scheme exists for…
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…
An unconventional approach is applied to solve the one-dimensional Burgers' equation. It is based on spline polynomial interpolations and Hopf-Cole transformation. Taylor expansion is used to approximate the exponential term in the…
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…
We are interested in the life span and the asymptotic behaviour of the solutions to a system governing the motion of a pressureless gas, submitted to a strong, inhomogeneous magnetic field $ \e^{-1} B(x)$, of variable amplitude but fixed…
In this paper we study the analytic solutions of Burgers-type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation.…
Global well-posedness, existence of globally absorbing sets and existence of inertial manifolds is investigated for a class of diffusive Burgers equations. The class includes diffusive Burgers equation with nontrivial forcing, the…
In this work, we consider the stochastic Burgers-Huxley equation perturbed by multiplicative Gaussian noise, and discuss about the global solvability results and asymptotic behavior of solutions. We show the existence of a global strong…
We construct global-in-time weak solutions to the pressureless Euler alignment system posed on the whole line and supplemented with initial conditions, where an initial density is an arbitrary, nonnegative, bounded, and integrable function…
The large-time behavior of solutions to Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context…
We present a computer assisted method for proving the existence of globally attracting fixed points of dissipative PDEs. An application to the viscous Burgers equation with periodic boundary conditions and a forcing function constant in…
When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets…
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…
We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper…