Non-standard shocks in the Buckley-Leverett equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:428

Article

Kalisch, Henrik¹  Marovich, Darko²  Nordbotten, Jan M.¹ 

[1] Univ Bergen, Dept Math, N-5020 Bergen, Norway

[2] Univ Montenegro, Fac Math, Cetinjski Put Bb, Montenegro

关键词: Conservation laws;    Delta shocks;    Riemann problem;    Weak asymptotics;    Traveling waves;   

DOI  :  10.1016/j.jmaa.2015.03.041

来源: Elsevier

【 摘 要 】

It is shown how delta shock waves which consist of Dirac delta distributions and classical shocks can be used to construct non-monotone solutions of the Buckley Leverett equation. These solutions are interpreted using a recent variational definition of delta shock waves in which the Rankine Hugoniot deficit is explicitly accounted for [6]. The delta shock waves are also limits of approximate solutions constructed using a recent extension of the weak asymptotic method to complexvalued approximations [15]. Finally, it is shown how these non-standard shocks can be fitted together to construct similarity and traveling-wave solutions which are non-monotone, but still admissible in the sense that characteristics either enter or are parallel to the shock trajectories. (C) 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (littp://creativecommons.org/licenses/by/4.0/).

【 授权许可】

Free