Nonlinear Self-Adjointness and Generalized Conserved Quantities of the Inviscid Burgers’ Equation with Nonlinear Source

2016 ◽  
Vol 3 (2) ◽  
pp. 963-970
Author(s):  
Muhammad Alim Abdulwahhab
Keyword(s):  
Burgers Equation ◽  
Conserved Quantities ◽  
Nonlinear Source ◽  
Inviscid Burgers Equation

On the Lie point symmetry analysis and solutions of the inviscid Burgers equation

Pramana ◽  
2011 ◽  
Vol 77 (3) ◽  
pp. 407-414 ◽  
Author(s):  
MUHAMMAD A ABDULWAHHAB ◽  
ASHFAQUE H BOKHARI ◽  
A H KARA ◽  
F D ZAMAN
Keyword(s):  
Burgers Equation ◽  
Symmetry Analysis ◽  
Point Symmetry ◽  
Inviscid Burgers Equation ◽  
Lie Point Symmetry

A Staggered Discontinuous Galerkin Method with Local TV Regularization for the Burgers Equation

2015 ◽  
Vol 8 (4) ◽  
pp. 451-474 ◽  
Author(s):  
Hiu Ning Chan ◽  
Eric T. Chung
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Discontinuous Galerkin ◽  
Numerical Approximation ◽  
Burgers Equation ◽  
Smooth Solutions ◽  
Regularization Technique ◽  
Tv Regularization ◽  
Inviscid Burgers Equation ◽  
Staggered Discontinuous Galerkin Method

AbstractThe staggered discontinuous Galerkin (SDG) method has been recently developed for the numerical approximation of partial differential equations. An important advantage of such methodology is that the numerical solution automatically satisfies some conservation properties which are also satisfied by the exact solution. In this paper, we will consider the numerical approximation of the inviscid Burgers equation by the SDG method. For smooth solutions, we prove that our SDG method has the properties of mass and energy conservation. It is well-known that extra care has to be taken at locations of shocks and discontinuities. In this respect, we propose a local total variation (TV) regularization technique to suppress the oscillations in the numerical solution. This TV regularization is only performed locally where oscillation is detected, and is thus very efficient. Therefore, the resulting scheme will preserve the mass and energy away from the shocks and the numerical solution is regularized locally near shocks. Detailed description of the method and numerical results are presented.

scholarly journals Systems of Sticky Particles Governed by Burgers' Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Octave Moutsinga
Keyword(s):  
Lebesgue Measure ◽  
Entropy Solution ◽  
Burgers Equation ◽  
Velocity Function ◽  
Mass Distributions ◽  
Inviscid Burgers Equation ◽  
Sticky Particles

We show the existence of two sticky particles models with the same velocity function ut(x) which is the entropy solution of the inviscid Burgers' equation. One of them is governed by the set of discontinuity points of u0. Thus, the trajectories t↦Xt coincide; however one has different mass distributions ∂xut=du0∘Xt-1 and λ∘Xt-1. Here, λ denotes the Lebesgue measure.

scholarly journals Inviscid Burgers’ Equation and Riemann Waves in Optics

2016 ◽  
Author(s):  
B. Wetzel ◽  
D. Bongiovanni ◽  
M. Kues ◽  
Y. Hu ◽  
Z. Chen ◽  
...  
Keyword(s):  
Burgers Equation ◽  
Inviscid Burgers Equation ◽  
Riemann Waves
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