For more information about this meeting, contact Hope Shaffer, Jinchao Xu, Kris Jenssen.
| Title: | Weakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | David Levermore, University of Maryland |
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| Abstract: |
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| Hyperbolic-parabolic systems have spatially homogeneous
stationary solutions. When the dissipation is weak, one can derive
weakly nonlinear-dissipative approximations that govern perturbations
of these solutions. These approximations are quadratically nonlinear.
Up to a linear transformation, they are independent of the dependent
variables used to express the original system. When the original
system has an entropy, the approximation is formally dissipative in a
natural Hilbert space. We show that under a mild structural hypothesis,
this approximation has global weak solutions for all initial data in that
Hilbert space. This theory applies to the compressible Navier-Stokes
system. The resulting approximate system is an incompressible
Navier-Stokes system coupled to equations that govern the acoustic modes.
The solution of this approximate system is unique if the incompressible
modes are uniquely determined. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 04 / 04 / 2008 |
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| Time: | 03:35pm - 04:25pm |
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