In this paper, we discuss some principles on the selection of the solutions of a special vectorial Hamilton-Jacobi system defined by (1.1) below. We first classify the equivalent solutions based on a wellknown construction and then discuss some selection principles using intuitive descriptions of coarseness or maximality of solutions. We also discuss a selection principle based on comparison of...

We study solutions of the system of PDE Dψ(vt) = DivDF (Dv), where ψ and F are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties of solutions that allow us to verify partial regularity when F is quadratic and characterize the large time limits of weak solutions. Special consideration is also given to systems that a...

A theory of drop-wise addition polymerization is developed. Because of the linear growth of the reaction volume V , the system gives rise to a new type of distribution function for cyclic species that can be expressed by the sum of two terms: the conventional distribution term and a extra term due to the dilution effect. The present result is an extension of the conventional homogeneous polymer...