Displaying similar documents to “Hyperbolic equations and systems with discontinuous coefficients or source terms”

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.

Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems

Jean-François Coulombel, Olivier Guès (2010)

Annales de l’institut Fourier

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We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optimal energy estimate in Sobolev spaces showing that losses of derivatives must occur from the...

Hyperbolic equations and SBV functions

Camillo De Lellis (2010)

Journées Équations aux dérivées partielles

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In this article we survey some recent results in the regularity theory of admissible solutions to hyperbolic conservation laws and Hamilton-Jacobi equations.