Displaying similar documents to “Lecture notes : Stability of Noncharacteristic Viscous Boundary Layers”

Finite differences and boundary element methods for non-stationary viscous incompressible flow

Werner Varnhorn (1994)

Banach Center Publications

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We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation...

Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations

Tomasz Człapiński (1992)

Annales Polonici Mathematici

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Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.

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.