02193nas a2200109 4500008004300000245008700043210006900130520180600199100002302005700001902028856003602047 2009 en_Ud 00aThe boundary Riemann solver coming from the real vanishing viscosity approximation0 aboundary Riemann solver coming from the real vanishing viscosity3 aWe study the limit of the hyperbolic-parabolic approximation $$ \\\\begin{array}{lll} v_t + \\\\tilde{A} ( v, \\\\, \\\\varepsilon v_x ) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in R^N\\\\\\\\ \\\\tilde \\\\beta (v (t, \\\\, 0)) = \\\\bar g \\\\\\\\ v (0, \\\\, x) = \\\\bar v_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nThe function $\\\\tilde \\\\beta$ is defined in such a way to guarantee that the initial boundary value problem is well posed even if $\\\\tilde \\\\beta$ is not invertible.\\nThe data $\\\\bar g$ and $\\\\bar v_0$ are constant. When $\\\\tilde B$ is invertible, the previous problem takes the simpler form $$ \\\\left\\\\{ \\\\begin{array}{lll} v_t + \\\\tilde{A} \\\\big( v, \\\\, \\\\varepsilon v_x \\\\big) v_x = \\\\varepsilon \\\\tilde{B}(v ) v_{xx} \\\\qquad v \\\\in \\\\mathbb{R}^N\\\\\\\\ v (t, \\\\, 0) \\\\equiv \\\\bar v_b \\\\\\\\ v (0, \\\\, x) \\\\equiv \\\\bar{v}_0. \\\\\\\\ \\\\end{array} \\\\right. $$\\nAgain, the data $\\\\bar v_b$ and $\\\\bar v_0$ are constant. The conservative case is included in the previous formulations. It is assumed convergence of the v, smallness of the total variation and other technical hypotheses and it is provided a complete characterization of the limit. The most interesting points are the following two. First, the boundary characteristic case is considered, i.e. one eigenvalue of $\\\\tilde A$ can be 0.\\n Second, as pointed out before we take into account the possibility that $\\\\tilde B$ is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if it is not satisfied, then pathological behaviours may occur.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/183100319nas a2200085 4500008004300000245006900043210006200112100002300174856003600197 2006 en_Ud 00aOn Bressan\\\'s conjecture on mixing properties of vector fields0 aBressans conjecture on mixing properties of vector fields1 aBianchini, Stefano uhttp://hdl.handle.net/1963/180600394nas a2200109 4500008004300000245005900043210005900102260004300161100002300204700002100227856003600248 2000 en_Ud 00aBV solutions for a class of viscous hyperbolic systems0 aBV solutions for a class of viscous hyperbolic systems bIndiana University Mathematics Journal1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/3194