Uniqueness of the Solutions of ut=Δum and ut=Δum-up with Initial Datum a Measure: the Fast Diffusion Case

Abstract

In this paper, we study the Cauchy problems u_t = Δu^m \quad u(x, 0) = μ and u_t = Δu^m - u^p \quad u(x, 0) = μ where p > 0, m > (1 - \frac{α}{n})^+ and μ is a finite Radon measure. We prove the uniqueness of solution and the existence of solution.