scholarly journals The stability of the shock profiles of the Burgers' equation

1998 ◽  
Vol 11 (5) ◽  
pp. 97-101 ◽  
Author(s):  
S. Engelberg
Keyword(s):  
Burgers Equation ◽  
Shock Profiles ◽  
The Stability

STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS

1995 ◽  
Vol 05 (03) ◽  
pp. 279-296 ◽  
Author(s):  
MING MEI
Keyword(s):  
Conservation Laws ◽  
Decay Rates ◽  
Asymptotically Stable ◽  
Time Decay ◽  
Shock Condition ◽  
Viscous Conservation Laws ◽  
Time Decay Rates ◽  
Shock Profiles ◽  
Degenerate Shock ◽  
The Stability

This paper is to study the stability of shock profiles for nonconvex scalar viscous conservation laws with the nondegenerate and the degenerate shock conditions by means of an elementary energy method. In both cases, the shock profiles are proved to be asymptotically stable for suitably small initial disturbances. Moreover, in the case of nondegenerate shock condition, time decay rates of asymptotics are also obtained.

A FDM for Burgers’ Equation on Unbounded Domains Using High-Order Artificial Boundary Conditions

2017 ◽  
Vol 865 ◽  
pp. 233-238
Author(s):  
Quan Zheng ◽  
Yu Feng Liu
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Unbounded Domain ◽  
Burgers Equation ◽  
High Order ◽  
Computational Domain ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Second Order Convergence ◽  
The Stability

Burgers’ equation on an unbounded domain is an important mathematical model to treat with some external problems of fluid materials. In this paper, we study a FDM of Burgers’ equation using high-order artificial boundary conditions on the unbounded domain. First, the original problem is converted into the heat equation on an unbounded domain by Hopf-Cole transformation. Thus the difficulty of nonlinearity of Burgers’ equation is overcome. Second, high-order artificial boundary conditions are given by using Padé approximation and Laplace transformation. And the conditions confine the heat equation onto a bounded computational domain. Third, we prove the solutions of the resulting heat equation and Burgers’ equation are both stable. Fourth, we establish the FDM for Burgers’ equation on the bounded computational domain. Finally, a numerical example demonstrates the stability, the effectiveness and the second-order convergence of the proposed method.

On the Stability of a Monotone Difference Scheme for the Burgers Equation

2005 ◽  
Vol 41 (7) ◽  
pp. 1003-1009 ◽  
Author(s):  
P. P. Matus ◽  
G. L. Marcinkiewicz
Keyword(s):  
Difference Scheme ◽  
Burgers Equation ◽  
The Stability

scholarly journals Stability of Traveling Waves to a Burgers Equation with 2nd-Order Nonlinear Diffusion

2022 ◽  
Vol 4 (1) ◽  
pp. 77-85
Author(s):  
Mohammad Ghani
Keyword(s):  
Asymptotic Stability ◽  
Small Perturbation ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Nonlinear Diffusion ◽  
Wave Amplitude ◽  
Energy Estimate ◽  
Burgers Equation ◽  
Original Equation ◽  
The Stability

We are interested in the study of asymptotic stability for Burgers equation with second-order nonlinear diffusion. We first transform the original equation by the ansatz transformation to establish the existence of traveling wave. We further employ the energy estimate under small perturbation and arbitrary wave amplitude. This energy estimate is then used to establish the stability.

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