Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/8305
Title: SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension
Authors: Bianchini, Stefano
Yu, Lei
Keywords: hyperbolic conservation lawsSBV-like regularwave-front tracking
Issue Date: 2012
Publisher: EUT Edizioni Università di Trieste
Source: Stefano Bianchini and Lei Yu, "SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 44 (2012), pp. 439–472.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
44 (2012)
Abstract: 
We prove the SBV regularity of the characteristic speed of the scalar hyperbolic conservation law and SBV-like regularity of the eigenvalue functions of the Jacobian matrix of flux function for general hyperbolic systems of conservation laws. More precisely, for the equation
$$
u_t + f(u)_x = 0, \quad u : \mathbb{R}^+ \times \mathbb{R} \to \Omega \subset \mathbb{R}^N,
$$
we only assume that the flux $f$ is a $C^2$ function in the scalar case ($N=1$) and Jacobian matrix $Df$ has distinct real eigenvalues in the system case $(N\geq 2)$. We show that for the scalar equation $f'(u)$ belongs to the SBV space, and for system of conservation laws the $i$-th component of $D_x\lambda_i(u)$
has no Cantor part, where $\lambda_i$ is the $i$-th eigenvalue of the matrix $Df$.
Type: Article
URI: http://hdl.handle.net/10077/8305
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.44 (2012)

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