The interaction of rarefaction waves of a two-dimensional nonlinear wave system. (April 2015)

• Record Type: Journal Article
• Authors: Hu, Yanbo; Wang, Guodong
• Is Part Of: Nonlinear analysis. Volume 22(2015)
• Page Start: 1
• Page End: 15
• Publication Date: 2015-04
• Subjects: Nonlinear wave system -- Two-dimensional Riemann problem -- Degenerate Goursat-type problem -- Interaction of rarefaction waves; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.07.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with a two-dimensional Riemann problem for the nonlinear wave system which gives rise to an interaction of two planar rarefaction waves. This problem comes from the expansion of a wedge of gas with constant velocity into vacuum, which is often interpreted as the dam collapse problem in hydraulics. We establish the global existence of smooth solutions in the interaction region of rarefaction waves up to a non-trivial vacuum boundary.