Global structure instability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary |
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Authors: | Zhi-Qiang Shao |
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Institution: | Department of Mathematics, Fuzhou University, Fuzhou 350002, China |
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Abstract: | This work is a continuation of our previous work Z.-Q. Shao, D.-X. Kong, Y.-C. Li, Shock reflection for general quasilinear hyperbolic systems of conservation laws, Nonlinear Anal. TMA 66 (1) (2007) 93-124]. In this paper, we study the global structure instability of the Riemann solution containing shocks, at least one rarefaction wave for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the nonexistence of global piecewise C1 solution to a class of the mixed initial-boundary value problem for general n×n quasilinear hyperbolic systems of conservation laws on the quarter plane. Our result indicates that this kind of Riemann solution mentioned above for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary is globally structurally unstable. Some applications to quasilinear hyperbolic systems of conservation laws arising from physics and mechanics are also given. |
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Keywords: | Mixed initial-boundary value problem Quasilinear hyperbolic systems of conservation laws Genuinely nonlinear Rarefaction wave Blowup Global structure instability |
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