PDE Seminar

Title: On the Approximation of Conservation Laws by Vanishing Viscosity
Speaker: Carlotta Donadello
Speaker Info: SISSA, Trieste, Italy
Brief Description:
Special Note:

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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