Abstract
We study the asymptotic behavior of the solution of the initial and initial-boundary value problem of hyperbolic conservation laws when the initial and boundary data have bounded total variation. It is shown that the solution converges to the linear superposition of traveling waves, shock waves and rarefaction waves. The strength and speed of these waves depend only on the values of the data at infinity.
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Communicated by J. Glimm
Results obtained at the Courant Institute of Mathematical Sciences, New York University while the author was a Visiting Member at the Institute; this work was supported by the National Science Foundation, Grant NSF-MCS 76-07039
On leave from the University of Maryland, College Park, USA
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Liu, TP. Large-time behavior of solutions of initial and initial-boundary value problems of a general system of hyperbolic conservation laws. Commun.Math. Phys. 55, 163–177 (1977). https://doi.org/10.1007/BF01626518
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DOI: https://doi.org/10.1007/BF01626518