Viscous–capillary traveling waves associated with classical and nonclassical shocks in van der Waals fluids. (June 2018)

• Record Type: Journal Article
• Authors: Hiep, Nguyen Huu; Thanh, Mai Duc; Huy, Nguyen Dinh
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 107
• Page End: 127
• Publication Date: 2018-06
• Subjects: Traveling wave -- van der Waals fluid -- Classical shock -- Nonclassical shock -- Viscosity -- Capillarity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.10.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We present in this work existence results for various types of diffusive–dispersive traveling waves associated with shock waves with the same shock speed in van der Waals fluids. For any shock satisfies a single entropy inequality, there exist corresponding traveling waves with suitable choices of viscosity and capillarity coefficients. The shock may be a classical shock, a nonclassical shock satisfying Lax's shock inequalities, or a nonclassical shock violating Lax's shock inequalities. Therefore, shock waves satisfying a single entropy inequality are also admissible under the criterion of vanishing viscosity/capillarity effects.