High-resolution numerical algorithm for one-dimensional scalar conservation laws with a constrained solution

2012 ◽  
Vol 52 (3) ◽  
pp. 400-410
Author(s):  
V. M. Goloviznin ◽  
A. A. Kanaev
Keyword(s):  
High Resolution ◽  
Conservation Laws ◽  
Numerical Algorithm ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Scalar Conservation

One-Dimensional Scalar Conservation Laws with Regulated Data

2020 ◽  
Vol 52 (3) ◽  
pp. 3114-3130
Author(s):  
Helge Kristian Jenssen ◽  
Johanna Ridder
Keyword(s):  
Conservation Laws ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Scalar Conservation

scholarly journals Fractional BV spaces and applications to scalar conservation laws

2014 ◽  
Vol 11 (04) ◽  
pp. 655-677 ◽  
Author(s):  
C. Bourdarias ◽  
M. Gisclon ◽  
S. Junca
Keyword(s):  
Conservation Laws ◽  
Stability Result ◽  
Entropy Solutions ◽  
Smoothing Effect ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Regular Functions ◽  
Bv Functions ◽  
Scalar Conservation ◽  
First Time

We obtain new fine properties of entropy solutions to scalar nonlinear conservation laws. For this purpose, we study the "fractional BV spaces" denoted by BVs(ℝ) (for 0 < s ≤ 1), which were introduced by Love and Young in 1937 and closely related to the critical Sobolev space Ws,1/s(ℝ). We investigate these spaces in connection with one-dimensional scalar conservation laws. The BVs spaces allow one to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with BVs initial data. Furthermore, for the first time, we get the maximal Ws,p smoothing effect conjectured by Lions, Perthame and Tadmor for all nonlinear (possibly degenerate) convex fluxes.

scholarly journals On the spreading of characteristics for non-convex conservation laws

2001 ◽  
Vol 131 (4) ◽  
pp. 909-925 ◽  
Author(s):  
Helge Kristian Jenssen ◽  
Carlo Sinestrari
Keyword(s):  
Conservation Laws ◽  
Error Term ◽  
Scalar Conservation Laws ◽  
One Dimensional ◽  
Flux Function ◽  
Characteristic Speed ◽  
Convex Case ◽  
Lipschitz Estimate ◽  
Scalar Conservation ◽  
Hölder Estimate

We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the flux function has one point of inflection. It is well known that in the convex case the characteristic speed satisfies a one-sided Lipschitz estimate. Using Dafermos' theory of generalized characteristics, we show that the characteristic speed in the non-convex case satisfies an Hölder estimate. In addition, we give a one-sided Lipschitz estimate with an error term given by the decrease of the total variation of the solution.

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