LAURA V. SPINOLO

Notes on the study of the viscous approximation of hyperbolic problems via ODE analysis

Pages: 151-188
Received: 28 October 2009   
Accepted: 20 January 2010
Mathematics Subject Classification (2010): 35L65, 37D10, 34A34, 35M30.

Keywords: Traveling waves, boundary layers, vanishing viscosity, invariant manifolds, viscous profiles, mixed hyperbolic-parabolic systems, Navier-Stokes equation, ordinary differential equations with singularity.

Abstract: These notes describe some applications of the analysis of ordinary differential equations to the study of the viscous approximation of conservation laws in one space dimension. The exposition mostly focuses on the analysis of invariant manifolds like the center manifold and the stable manifold. The last section addresses a more specific issue and describes a possible way of extending the notions of center and stable manifold to some classes of singular ordinary differential equations arising in the study of the Navier-Stokes equation in one space variable.