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 ut + f(u)x = 0, u : R + × R → Ω ⊂ RN , we only assume that the flux f is a C2 function in the scalar case (N = 1) and Jacobian matrix Df has distinct real eigenvalues in the system case (N ≥ 2). Using a modification of the main decay estimate in [8] and the localization method applied in [17], we show that for the scalar equation f0(u) belongs to the SBV space, and for system of conservation laws the i-th component of Dxλi(u) has no Cantor part, where λi is the i-th eigenvalue of the matrix Df.
SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension / Bianchini, S.; Yu, L.. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 44:(2012), pp. 439-472.
SBV-like regularity for general hyperbolic systems of conservation laws in one space dimension
Bianchini, S.;
2012-01-01
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 ut + f(u)x = 0, u : R + × R → Ω ⊂ RN , we only assume that the flux f is a C2 function in the scalar case (N = 1) and Jacobian matrix Df has distinct real eigenvalues in the system case (N ≥ 2). Using a modification of the main decay estimate in [8] and the localization method applied in [17], we show that for the scalar equation f0(u) belongs to the SBV space, and for system of conservation laws the i-th component of Dxλi(u) has no Cantor part, where λi is the i-th eigenvalue of the matrix Df.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.