355 eng article 1 2020-06-19 2020-10-27 -- In this work, we analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to an optimal control problem. As a by-product, we obtain the long-time behavior of the solution to the associated Hamilton-Jacobi-Bellman equation. In order to carry out our study, we use the setting of a finite-dimensional linear-quadratic optimal control problem, for which the turnpike property is well understood. We prove that, when the time horizon T tends to infinity, the value function converges to a travelling-front like solution of the form W(x) + c T + λ. In addition, we provide a control interpretation of each of these three terms in the spirit of the turnpike theory. Finally, we compare this asymptotic decomposition with the existing results on long-time behavior for Hamilton-Jacobi equations. We stress that in our case, the Hamiltonian is not coercive in the momentum variable, a case rarely considered in the classical literature about Hamilton-Jacobi equations. under review false false 2 Creative Commons - CC BY - Namensnennung 4.0 International Carlos Esteve H Kouhkouh Dario Pighin Enrique Zuazua eng uncontrolled Optimal control problems eng uncontrolled long-time behavior eng uncontrolled the turnpike property eng uncontrolled Hamilton-Jacobi-Bellman equations eng uncontrolled linear-quadratic C03 https://opus4.kobv.de/opus4-trr154/files/355/10-TurnpikeLongTimeBeh.pdf