SINGULAR INFINITE HORIZON CALCULUS OF VARIATIONS.APPLICATIONS TO FISHERIES MANAGEMENT

摘要

We consider a calculus of variations problem in infinite horizon linearwith respect to the velocities. In our case the admissible curves stay in a boundedinterval and we prove that the MRAP (Most Rapid Approach Pathes) from anyinitial conditions to the solutions of the (algebraic) Euler-Lagrange equation areoptimal. We use a result on the uniqueness of the solution of a Hamilton-Jacobiequation. We propose some new and straightforward proofs. Particularly weshow that boundary conditions, that are essential for the uniqueness, are satisfiedunder some assumptions that we detail. Finally we underline the limits for theapplications (fisheries examples) of the established results.