Abstract | Keywords | Export | Availability | Bookmark

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts. Williams’ lecture describes the stability of multidimensional viscous shocks: the small viscosity limit, linearization and conjugation, Evans functions, Lopatinski determinants etc. Zumbrun discusses planar stability for viscous shocks with a realistic physical viscosity, necessary and sufficient conditions for nonlinear stability, in analogy to the Lopatinski condition obtained by Majda for the inviscid case.

Differential equations, Hyperbolic --- Shock waves --- Equations différentielles hyperboliques --- Congresses. --- Mathematics --- Congrès --- Differential equations, Hyperbolic -- Congresses. --- Electronic books. -- local. --- Shock waves -- Mathematics -- Congresses. --- Calculus --- Physical Sciences & Mathematics --- Mathematics. --- Partial differential equations. --- Numerical analysis. --- Continuum physics. --- Partial Differential Equations. --- Classical Continuum Physics. --- Numerical Analysis. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Mathematical analysis --- Partial differential equations --- Math --- Science --- Shock (Mechanics) --- Waves --- Differential equations, partial. --- Classical and Continuum Physics.