Related papers: Complex-valued Burgers and KdV-Burgers equations
An initial-boundary value problem for a generalized KdV equation posed on a half-line is considered. Existence and uniqueness of global regular solutions for arbitrary smooth initial data are established.
We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized…
Relativistic complex Burgers-Schr\"odinger and Nonlinear Schr\"odinger equations are constructed. In the non-relativistic limit they reduce to the standard Burgers and NLS equations respectively and are integrable at any order of…
A new three-dimensional (3D) equation is proposed, which is formed like Burgers' equation by starting with the 3D incompressible Navier-Stokes equations (NSE) and eliminating the pressure and the divergence-free constraint, but instead the…
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 prove that the stochastic Burgers equation on $\mathbf{R}^{d}$, $d<4$, forced by gradient noise that is white in time and smooth in space, admits spacetime-stationary solutions. These solutions are thus the gradients of solutions to the…
We consider the KdV-Burgers equation and its linear version in presence of a delay feedback. We prove well-posedness of the models and exponential decay estimates under appropriate conditions on the damping coefficients. Our arguments rely…
We investigate the stability of traveling front solutions to nonlinear diffusive-dispersive equations of Burgers type, with a primary focus on the Korteweg-de Vries-Burgers (KdVB) equation, although our analytical findings extend more…
We study the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known that the system admits solutions which blow up in finite time…
The formation of singularities in finite time in non-local Burgers' equations, with time-fractional derivative, is studied in detail. The occurrence of finite time singularity is proved, revealing the underlying mechanism, and precise…
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…
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…
The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value…
We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long"…
In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.
Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the time-averaged patterns for the case of stepwise fixed boundary conditions. Our results show…
We study the inviscid Burgers equation in the presence of spatially periodic potential force. We prove that for foliated initial value problem there are always solutions developing shocks in a finite time. We give an application of this…
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…
An initial-boundary value in a strip with homogeneous Dirichlet boundary conditions for two-dimensional Zakharov-Kuznetsov-Burgers equation is considered. Results on global well-posedness and long-time decay of solutions in Sobolev spaces…
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.…