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Free Boundary Problems for Nonlinear Wave Systems: Interacting Shocks (2003)
| Content Provider | CiteSeerX |
|---|---|
| Author | Canic, Suncica Keyfitz, Barbara Lee Kim, Eun Heui |
| Abstract | We prove the existence of a global solution for a family of two-dimensional Riemann problems for compressible flow modeled by the nonlinear wave system. The initial constant states are separated by two jump discontinuities, x = a y, which develop into two interacting shock waves. The solution is symmetric about the y-axis and on each side of the y-axis the solution consists of an incident shock, a reflected compression wave and a Mach stem. This has a clear analogy with the problem of shock reflection by a ramp. We prove the existence of a global self-similar solution with this structure, which need not be close to the piecewise constant solution which occurs with collinear shocks. A novel feature is the capability to deal analytically with a Mach stem. The difficulties associated with the analysis of solutions containing Mach stems include (1) loss of obliqueness in the derivative boundary condition corresponding to the jump conditions across the Mach stem, and (2) analysis of the interaction between incident wave, Mach stem and reflected wave, as triple shock points cannot occur. We use barrier functions to show that for large values of a the reflected wave is a continuous weak compression wave. This approach gives a new transition criterion for the boundary between two qualitatively different solution structures, and demonstrates that elliptic estimates may be important in the analysis of transition criteria in hyperbolic wave interactions. |
| File Format | |
| Publisher Date | 2003-01-01 |
| Access Restriction | Open |
| Subject Keyword | Mach Stem Nonlinear Wave System Interacting Shock Free Boundary Problem Transition Criterion Derivative Boundary Condition Collinear Shock Two-dimensional Riemann Problem Different Solution Structure Global Self-similar Solution Jump Condition Shock Wave Elliptic Estimate Reflected Compression Wave Incident Wave Large Value Novel Feature Initial Constant State Shock Reflection Incident Shock Continuous Weak Compression Wave Global Solution Jump Discontinuity Triple Shock Point New Transition Criterion Reflected Wave Barrier Function Compressible Flow Piecewise Constant Solution Clear Analogy |
| Content Type | Text |
