Some properties of evolution equation for homogeneous nucleation period under the smooth behavior of initial conditions

TL;DR

This paper analyzes the evolution equation for homogeneous nucleation, establishing solution uniqueness and existence under specific conditions, and clarifies the relationship between auxiliary and real problems in nucleation theory.

Contribution

It proves the uniqueness and existence of solutions for the evolution equation in homogeneous nucleation and demonstrates the equivalence between auxiliary and real problems.

Findings

Solution uniqueness and existence established

Equivalence between auxiliary and real problems shown

Properties of the evolution equation analyzed

Abstract

The properties of the evolution equation have been analyzed. The uniqueness and the existence of solution for the evolution equation with special value of parameter characterizing intensity of change of external conditions, of the corresponding iterated equation have been established. On the base of these facts taking into account some properties of behavior of solution the uniqueness of the equation appeared in the theory of homogeneous nucleation has been established. The equivalence of auxiliary problem and the real problem is shown.