scholarly journals Convergence of a misanthrope process to the entropy solution of 1D problems

2012 ◽  
Vol 122 (11) ◽  
pp. 3648-3679 ◽  
Author(s):  
R. Eymard ◽  
M. Roussignol ◽  
A. Tordeux
Keyword(s):  
Entropy Solution ◽  
Misanthrope Process

scholarly journals ON A STOCHASTIC FIRST-ORDER HYPERBOLIC EQUATION IN A BOUNDED DOMAIN

2009 ◽  
Vol 12 (04) ◽  
pp. 613-651 ◽  
Author(s):  
GUY VALLET ◽  
PETRA WITTBOLD
Keyword(s):  
Hyperbolic Equation ◽  
Bounded Domain ◽  
Entropy Solution ◽  
Stochastic Perturbation ◽  
Dirichlet Condition ◽  
First Order ◽  
Scalar Conservation Law ◽  
Order Hyperbolic Equation ◽  
Scalar Conservation ◽  
Entropy Formulation

In this paper, we are interested in the stochastic perturbation of a first-order hyperbolic equation of nonlinear type. In order to illustrate our purposes, we have chosen a scalar conservation law in a bounded domain with homogeneous Dirichlet condition on the boundary. Using the concept of measure-valued solutions and Kruzhkov's entropy formulation, a result of existence and uniqueness of the entropy solution is given.

scholarly journals A Bhatnagar–Gross–Krook approximation to scalar conservation laws with discontinuous flux

2010 ◽  
Vol 140 (5) ◽  
pp. 953-972 ◽  
Author(s):  
F. Berthelin ◽  
J. Vovelle
Keyword(s):  
Conservation Laws ◽  
Entropy Solution ◽  
Limit Problem ◽  
Scalar Conservation Laws ◽  
First Order ◽  
The Cauchy Problem ◽  
Discontinuous Flux ◽  
Scalar Conservation ◽  
Bgk Approximation ◽  
Well Posed

AbstractWe study the Bhatnagar–Gross–Krook (BGK) approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy problem for the BGK approximation is well posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.

Entropy solution at concave corners and ridges, and volume boundary layer tangential adaptivity

2019 ◽  
Vol 376 ◽  
pp. 1-19 ◽  
Author(s):  
R. Aubry ◽  
B.K. Karamete ◽  
E.L. Mestreau ◽  
C. Jones ◽  
S. Dey
Keyword(s):  
Boundary Layer ◽  
Entropy Solution

GLOBAL SOLUTION FOR ROTATING COMPRESSIBLE PLASMA FLOW WITH LARGE DATA

2007 ◽  
Vol 04 (02) ◽  
pp. 351-368
Author(s):  
DEHUA WANG ◽  
ZEJUN WANG
Keyword(s):  
Approximate Solution ◽  
Plasma Flow ◽  
Entropy Solution ◽  
Uniform Estimate ◽  
Large Data ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Poisson Equations ◽  
Entropy Dissipation ◽  
Weak Entropy Solution

The initial boundary value problem for the Euler–Poisson equations of the two-dimensional compressible rotating plasma flow with large data in L∞ is studied in the isothermal case. The shock capturing method is used to construct the approximate solution. The uniform estimate and the H-1 estimate of the entropy dissipation measures are obtained, and the compensated compactness method is applied to show the convergence of the approximate solution. The nonlocal effect of the Poisson equation is analyzed. The limit of the approximate solution is a weak entropy solution. Therefore the global weak entropy solution in L∞ to the Euler–Poisson equations for rotating plasma flow is constructed and the global existence is established.

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