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Exterior Differential Systems and the Method of Equivalence |
| May 05, 2008 to May 09, 2008 |
| Organized By: Jeanne Clelland, William F. Shadwick (Chair) and George Wilkens |
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| Return to Workshop Description |
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Hyperbolic Conservation Laws with Prescribed Eigencurves
Friday May 9, 2008
02:00PM - 03:00PM
Speakers:
Kris Jenssen
Abstract:
Hyperbolic Conservation Laws with Prescribed Eigencurves
Abstract: Motivated by recent examples of singular behavior in systems of hyperbolic conservation laws in one space dimension, we consider the following problem: Given $n$ vector fields $R_1,..., R_n$ in $\mathbb R^n$; determine if there exists an $n\times n$-system of hyperbolic conservation laws with a flux function whose Jacobian has the $R_i$ as right eigenvectors. We formulate this as a problem for the eigenvalues of the system. For $n\geq 3$ this typically gives an over-determined system of PDEs for the eigenvalues to which we apply Cartan-K\"a hler theory. Several concrete examples are also given. This is joint work with Irina Kogan (NCSU).
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