2007/12/01 by Silvia Faggian, Faggian, Silvia
Economics, Econometrics and Finance · Mathematics · #35B37. #49J15 #49J20 #Economic theories and models #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC #msc:35B37. #msc:49J15 #msc:49J20
paper · pdf · doi:10.48550/arxiv.0712.0025
arxiv created 2007/12/01 · openalex publication_date 2007/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run.