Generalized Young Measure Solutions for a Class of Quasilinear Parabolic Equations with Linear Growth

Abstract

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.