Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels

We study dispersive models of fluid flow in viscoelastic vessels, derived the blood flow. The unknowns are velocity axial direction and displacement vessel wall from rest. prove that one such model has a well-posed initial value problem, while we argue related instead an ill-posed problem; second case, still existence solutions analytic function spaces. Finally some periodic traveling waves.