Connections between symmetries and conservation laws.
Bluman, George (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Bluman, George (2005)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Olivier Glass (2005)
Journées Équations aux dérivées partielles
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Neves, Wladimir, Serre, Denis (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Danilov, Vladimir G. (2008)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zahran, Yousef Hashem (2006)
Novi Sad Journal of Mathematics
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Sanja Konjik (2005)
Publications de l'Institut Mathématique
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Frédéric Rousset (2002)
Journées équations aux dérivées partielles
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We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of Grenier and Rousset (2001), we replace the smallness condition obtained by energy methods in Goodman and Xin (1992) by a weaker spectral assumption.
Liu, Mingbin, Cheng, Zhixin (2007)
Revista Colombiana de Matemáticas
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Mitrovic, Darko, Susic, Jela (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Alberto Bressan (2002)
Journées équations aux dérivées partielles
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This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.