We establish here the global existence and uniqueness of admissible (both dissipative and conservative) weak solutions to a canonical asymptotic equation (∂t v + u∂x v + 1/2 v2 = 0, v = ∂xu) for weakly nonlinear solutions of a class of nonlinear variational wave equations with any L2(ℝ) initial datum. We use the method of Young measures and mollification techniques.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering