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NOTES ON THE STUDY OF THE VISCOUS APPROXIMATION OF
 

Summary: NOTES ON THE STUDY OF THE
VISCOUS APPROXIMATION OF
HYPERBOLIC PROBLEMS VIA
ODE ANALYSIS
LAURA V. SPINOLO
Preprint di Matematica N. 5
Ottobre 2009
NOTES ON THE STUDY OF THE VISCOUS APPROXIMATION OF
HYPERBOLIC PROBLEMS VIA ODE ANALYSIS
LAURA V. SPINOLO
Abstract. These notes describe some applications of the analysis of ordinary differen-
tial 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.
1. Introduction
In recent years, techniques coming from the study of ordinary differential equations (ODEs)
have been applied to the analysis of systems of conservation laws in one space dimension,

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics