Displaying similar documents to “Conservation laws of discrete Korteweg-de Vries equation.”

Viscous Limits for strong shocks of one-dimensional systems of conservation laws

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.

On the well posedness of vanishing viscosity limits

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.