Abstract: This chapter studies the existence and uniqueness of solutions of the Cauchy problem for the PME posed in the whole space, which take a Radon measure as initial data. Section 13.1 constructs limit solutions for data measures with the growth condition found as optimal in the previous chapter (in the non-negative case). The theory is continued in Section 13.2 where it is proven that any non-negative solution defined in a domain Q_T has a unique initial trace. In Sections 13.3 and 13.4, it is proved that the initial trace determines the solution in a unique way. This is a landmark in the theory of the PME and completes the basic theory of the Cauchy problem developed in previous chapters.

Keywords: Cauchy problem, PME, whole space, Radon measure, Pierre's uniqueness theorem,