caa a22 4500 388109114 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013111 doi S0308210500013111 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013111 Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes [Elektronische Daten] The Riemann initial value problem is studied for scalar conservation laws whose fluxes have a single inflection point. For a regularization consisting of balanced diffusive and dispersive terms, the travelling wave criterion is used to select admissible shocks. In some cases, the Riemann problem solution contains an undercompressive shock. The analysis is illustrated by exploring parameter space for the Buckley-Leverett flux. The boundary of the set of parameters for which there is a physical solution of the Riemann problem for all data is computed. Within the region of acceptable parameters, the solution hasseveral different forms, depending on the initial data; the different forms are illustrated by numerical computations. Qualitatively similar behaviour is observed in Lax-Wendroff approximations of solutions of the Buckley-Leverett equation with no dissipation or dispersion. Copyright © Royal Society of Edinburgh 1999 Hayes Brian Department of Mathematics, Duke University, Durham, NC 27708-0320, USA Shearer Michael Centre for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 733-754 0308-2105 129:4<733 1999 129 PRM https://doi.org/10.1017/S0308210500013111 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013111 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hayes Brian Department of Mathematics, Duke University, Durham, NC 27708-0320, USA NATIONALLICENCE 700 1- Shearer Michael Centre for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 733-754 0308-2105 129:4<733 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge