For more information about this meeting, contact Hope Shaffer, Jinchao Xu, Kris Jenssen.
| Title: | Shock Reflection-Diffraction, Transonic Flow, and Free Boundary Problems |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | Gui-Qiang Chen, Northwestern University |
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| Abstract: |
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| When a plane shock hits a wedge head on, it experiences a
reflection-diffraction process and then a self-similar reflected
shock moves outward as the original shock moves forward in time. The
complexity of reflection configurations was first reported by Ernst
Mach in 1878, and experimental, computational, and asymptotic
analysis has shown that various patterns of shock reflection may
occur, including regular and Mach reflection. However, most
fundamental issues for shock reflection have not been understood,
including the transition of the different patterns of shock
reflection, and there has been few rigorous mathematical result on
the global existence and structural stability of shock reflection,
especially for potential flow which has widely been used in
aerodynamics.
In this talk we will start with various shock reflection phenomena
and their fundamental scientific issues. Then we will describe how
the shock reflection problems can be formulated as free boundary
problems for nonlinear conservation laws of mixed-composite
hyperbolic-parabolic type. Finally we will discuss some recent
developments in attacking the shock reflection problems, including
the existence, regularity, and stability of global regular
configurations of shock reflection by wedges for potential flow.
The approach includes techniques to handle free boundary problems,
degenerate elliptic equations, and corner singularities, which is
highly motivated by experimental, computational, and asymptotic results.
This talk will be mainly based on joint work with M. Feldman. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 02 / 29 / 2008 |
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| Time: | 03:35pm - 04:25pm |
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