Author： Sinestrari C.
Publisher： Academic Press
ISSN： 0022-0396
Source： Journal of Differential Equations, Vol.134, Iss.2, 1997-03, pp. : 269-285
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Abstract
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.
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