  Using the generalized Young measure theory, we extend the theory of Young
measure solutions to a class of quasilinear parabolic equations with linear
growth, and introduce the concept of generalized Young measure solutions. We
prove the existence and uniqueness of the generalized Young measure solutions.
In addition, for the gradient flow of convex parabolic variational integral, we
show that the generalized Young measure solutions are equivalent to the strong
solutions.
