caa a22 4500 388108622 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500027487 doi S0308210500027487 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500027487 Mielke Alexander Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, D-30167 Hannover (mielke@ifam.uni-hannover.de) Flow properties for Young-measure solutions of semilinear hyperbolic problems [Elektronische Daten] [Alexander Mielke] For hyperbolic systems in one spatial dimension ∂tu + C∂xu = f(u), u(t, x) ∈ ℝd, we study sequences of oscillating solutions by their Young-measure limit, μ, and develop tools to study the evolution of μ directly from the Young measure, v, of the initial data. For d ≤ 2 we construct a flow mapping, St, such that μ(t) = St(v) is the unique Young-measure solution for initial value v. For d ≥ 3 we establish existence and uniqueness of Young measures that have product structure, that is the oscillations in direction of the Riemann invariants are independent. Counterexamples show that neither μ nor the marginal measures of the Riemann invariants are uniquely determined from v, except if a certain structural interaction condition for f is satisfied. We rely on ideas of transport theory and make use of the Wasserstein distance on the space of probability measures. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 85-123 0308-2105 129:1<85 1999 129 PRM https://doi.org/10.1017/S0308210500027487 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500027487 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Mielke Alexander Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, D-30167 Hannover (mielke@ifam.uni-hannover.de) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/1(1999), 85-123 0308-2105 129:1<85 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge