## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**Title:** On the Approximation of Conservation Laws by Vanishing Viscosity

**Speaker:** Carlotta Donadello

**Speaker Info:** SISSA, Trieste, Italy

**Brief Description:**

**Special Note**:

**Abstract:**

We consider a system of conservation laws in one space dimension, with fixed, bounded initial data. We suppose the flux function f to be
strictly convex and of class C^2. As shown by the analysis of Goodman and Xin (1992), in the case the solution, u, contains finitely many
non-interacting entropic shocks, its viscous approximations admit a singular perturbation expansion, i.e. they admit expansions in terms of powers of the
viscosity coefficient both in the region where u is smooth and near the shock discontinuities. In a joint work with prof. A. Bressan (PSU) we proved that
in the scalar case, i.e. when the system reduces to a single equation, a similar inner and outer expansion can still be performed for t>T, if for t>T
the solution u consists of an isolated shock. In this talk I'll discuss this result and I'll explain why a similar one for the vectorial case is
unlikely to hold. As an example I'll present some results concerning the transient behavior of a solution containing two interacting shocks of different
families.

**Date:** Thursday, May 15, 2008

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Laura Spinolo

**Contact email:** spinolo@math.northwestern.edu

**Contact Phone:** 847-467-1823

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