Viscous-capillary traveling waves associated with classical and nonclassical shocks in van der Waals fluids

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.