Regularization and persistence in nonlinear diffusion equations with measure initial data

In this paper, we study nonnegative Radon measure-valued solutions of the Cauchy– Dirichlet problem for ∂tu = Δφ(u) in a bounded domain with φ smooth, strictly increasing, and sublinear at infinity. Specific assumptions on the behavior of the second derivative of φ for large arguments are also made. Conditions are given under which parts of the initial measure persist, or solutions gain L1 (or even L∞) regularity for positive times. Constructive methods, comparison techniques and estimates of Aronson–B´enilan type are used.