ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 76N10, 76D05, 35M20 Jiang, Song, Institute of Applied Physics and Computational Mathematics, Beijing, China Large-time behavior of solutions to the equations of a onedimensional viscous polytropic ideal gas in unbounded domains The large-time behavior of solutions to the initial and initial boundary value problems for a one-dimensional viscous polytropic ideal gas in unbounded domains is investigated. Using a special cut-off function to localize the problem, we derive a local representation for the specific volume. With the help of the local representation, and certain new estimates for the temperature and the stress, and the weighted energy estimates, we prove that in any bounded interval, the specific volume is pointwise bounded from below and above for all t ≥ 0 and a generalized solution is convergent as time goes to infinity.