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A Connection between Viscous Profiles and Singular ODEs
Bianchini, Stefano
Spinolo, Laura V.
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 $0$.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
41 (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.
Languages
en
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