Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4007

 Title: A Connection between Viscous Profiles and Singular ODEs Authors: Bianchini, StefanoSpinolo, Laura V. Keywords: Mixed Hyperbolic-Parabolic SystemsSingular ODEBoundary LayersTraveling WavesNavier Stokes Equation Issue Date: 2009 Publisher: EUT Edizioni Università di Trieste Citation: Stefano Bianchini, Laura V. Spinolo, "A Connection between Viscous Profiles and Singular ODEs”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 41 (2009), pp. 35–41. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics41 (2009) Abstract: We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems in one space dimension. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form$\frac{dV}{dt} = \frac{1}{\zeta (V)} F(V).$ Here $V \in \mathbb{R}^d$ and the function $F$ takes values into $\mathbb{R}^d$ and is smooth. The real valued function $\zeta$ is as well regular: the equation is singular in the sense that $\zeta (V)$ can attain the value $0$. URI: http://hdl.handle.net/10077/4007 ISSN: 0049-4704 MS Classification 2000: 34A9935L6535M10 Appears in Collections: Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.41 (2009)

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