Instability of discontinuous traveling waves for hyperbolic balance laws

[摘要] It is known that scalar hyperbolic conservation laws with source term and periodic initial value have a property of Poincare-Bendixson type, namely the solutions converge either to a constant state or to a periodic traveling wave, which is necessarily discontinuous. In this paper we show that generically (with respect to the L(1) topology) the solutions exhibit a behaviour of the former type. We also show that, while the rate of convergence to a constant state is exponential, the convergence to a traveling wave can be arbitrarily slow. (C) 1997 Academic Press.

[发布日期] 1997-03-01