ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35B05, 35L65, 35L67 Härterich, Jörg, Freie Universität Berlin, Germany Heteroclinic Orbits Between Rotating Waves in Hyperbolic Balance Laws Scalar hyperbolic conservation laws with source terms

u_{t} + f(u)_{x} = g(u)

with x ∈ S^{1} possess a large number of rotating wave solutions with shocks. They can be classified via a set Z(u) ⊆ S^{1} where u takes a certain value. We look for solutions which exist globally in time and converge to different rotating waves as t → ±∞. It is known that such heteroclinic orbits from a rotating wave u_{1} to another wave u_{2} can exist only if Z(u_{2}) ⊆ Z(u_{1}). We show that this condition is also sufficient. Moreover, we describe the shock structure of the heteroclinic orbits.