@article {2007,
title = {BV instability for the Lax-Friedrichs scheme},
number = {SISSA;100/2004/M},
year = {2007},
abstract = {It is proved that discrete shock profiles (DSPs) for the Lax-Friedrichs scheme for a system of conservation laws do not necessarily depend continuously in BV on their speed. We construct examples of $2 \\\\times 2$-systems for which there are sequences of DSPs with speeds converging to a rational number. Due to a resonance phenomenon, the difference between the limiting DSP and any DSP in the sequence will contain an order-one amount of variation.},
url = {http://hdl.handle.net/1963/2335},
author = {Paolo Baiti and Alberto Bressan and Helge Kristian Jenssen}
}
@article {2006,
title = {An instability of the Godunov scheme},
journal = {Comm. Pure Appl. Math. 59 (2006) 1604-1638},
number = {arXiv.org;math/0502125v1},
year = {2006},
abstract = {We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes.},
doi = {10.1002/cpa.20141},
url = {http://hdl.handle.net/1963/2183},
author = {Alberto Bressan and Helge Kristian Jenssen and Paolo Baiti}
}
@article {2001,
title = {On the spreading of characteristics for non-convex conservation laws},
journal = {Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 909-925},
year = {2001},
publisher = {Cambridge University Press},
abstract = {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 H{\"o}lder 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.},
doi = {10.1017/S0308210500001189},
url = {http://hdl.handle.net/1963/3265},
author = {Helge Kristian Jenssen and Carlo Sinestrari}
}
@article {2000,
title = {On the convergence of Godunov scheme for nonlinear hyperbolic systems},
journal = {Chinese Ann. Math. B, 2000, 21, 269},
number = {SISSA;15/00/M},
year = {2000},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1473},
author = {Alberto Bressan and Helge Kristian Jenssen}
}
@article {1999,
title = {Blowup asymptotics for scalar conservation laws with a source},
journal = {Comm. in Partial Differential Equations 24 (1999) 2237-2261},
number = {SISSA;91/97/M},
year = {1999},
publisher = {Taylor and Francis},
doi = {10.1080/03605309908821500},
url = {http://hdl.handle.net/1963/3482},
author = {Helge Kristian Jenssen and Carlo Sinestrari}
}