Blowup of solutions to generalized Riemann problem for quasilinear hyperbolic systems of conservation laws

In this paper we study the global structure instability of Riemann solution u = U(x/t), containing at least one centred rarefaction wave, for the general nxn quasilinear hyperbolic system of conservation laws. We prove the non-existence of the global piecewise C-1 solution to a class of generalized Riemann problems, which can be regarded as a perturbation of the corresponding Riemann problem. This result shows that this kind of Riemann solution mentioned above is globally structurally unstable. Applications to quasilinear hyperbolic systems arising from physics and mechanics, particularly to surface waves in hyperelastic materials, are also given.