00820nas a2200121 4500008004300000245004900043210004800092520045600140100001700596700002100613700002800634856003600662 2007 en_Ud 00aBV instability for the Lax-Friedrichs scheme0 aBV instability for the LaxFriedrichs scheme3 aIt 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.1 aBaiti, Paolo1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/233500891nas a2200121 4500008004300000245004100043210003800084520054500122100002100667700002800688700001700716856003600733 2006 en_Ud 00aAn instability of the Godunov scheme0 ainstability of the Godunov scheme3 aWe 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.1 aBressan, Alberto1 aJenssen, Helge Kristian1 aBaiti, Paolo uhttp://hdl.handle.net/1963/218300970nas a2200121 4500008004300000245007300043210006500116260003100181520055000212100002800762700002200790856003600812 2001 en_Ud 00aOn the spreading of characteristics for non-convex conservation laws0 aspreading of characteristics for nonconvex conservation laws bCambridge University Press3 aWe 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 HÃ¶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.1 aJenssen, Helge Kristian1 aSinestrari, Carlo uhttp://hdl.handle.net/1963/326500395nas a2200109 4500008004100000245007400041210006700115260001800182100002100200700002800221856003600249 2000 en d00aOn the convergence of Godunov scheme for nonlinear hyperbolic systems0 aconvergence of Godunov scheme for nonlinear hyperbolic systems bSISSA Library1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/147300394nas a2200109 4500008004300000245006600043210006600109260002300175100002800198700002200226856003600248 1999 en_Ud 00aBlowup asymptotics for scalar conservation laws with a source0 aBlowup asymptotics for scalar conservation laws with a source bTaylor and Francis1 aJenssen, Helge Kristian1 aSinestrari, Carlo uhttp://hdl.handle.net/1963/3482