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, Stefano
Spinolo, Laura V.
Keywords: Mixed Hyperbolic-Parabolic SystemsSingular ODEBoundary LayersTraveling WavesNavier Stokes Equation
Issue Date: 2009
Publisher: EUT Edizioni Università di Trieste
Source: 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 Mathematics
41 (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
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.41 (2009)

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