Positively Invariant Regions for a Problem in Phase Transitions

摘要

Positively invariant regions for the system sub t + p(w) sub x = epsilon sub xx w sub t - v sub x = ew sub xx are constructed where p' < ), w< alpha, w>beta, P'(w) = 0, alpha < or = w < or = beta, e > 0. Such a choice of p is motivated by the Maxwell construction for a van der Waals fluid. The method of an analysis is a modification of earlier ideas . The results given here provide epsilon independent L at infinity bounds on the solution (w,v).