Displaying similar documents to “A controllability result for the 1 -D isentropic Euler 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.

A minicourse on global existence and blowup of classical solutions to multidimensional quasilinear wave equations

Serge Alinhac (2002)

Journées équations aux dérivées partielles

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The aim of this mini-course is twofold: describe quickly the framework of quasilinear wave equation with small data; and give a detailed sketch of the proofs of the blowup theorems in this framework. The first chapter introduces the main tools and concepts, and presents the main results as solutions of natural conjectures. The second chapter gives a self-contained account of geometric blowup and of its applications to present problem.