A Lagrangian Approach to Weakly Coupled Hamilton--Jacobi Systems
نویسندگان
چکیده
منابع مشابه
Singular perturbations of weakly coupled systems of Hamilton-Jacobi equations
In this paper we study singular perturbations of weakly coupled systems of elliptic equations. A model problem is given by small random perturbations of random evolution processes. In this setting we give a PDE proof of large deviation results, analogous to those studied in [5], [10, 11]. An essential tool in our approach is the weak KAM theory introduced in [15].
متن کاملAubry Sets for Weakly Coupled Systems of Hamilton-Jacobi Equations
We introduce the notion of Aubry set for weakly coupled systems of Hamilton–Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of globally strict critical subsolutions concentrates. As in the case of a single equation, we prove the existence of critical subsolutions which are strict and smooth outside the Aubry set. This allows us to derive in...
متن کاملHamilton-Jacobi approach to Berezinian singular systems
In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed for singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the HamiltonJacobi equation for such systems, analizing the singular case in order to obtain the equations of motion as total differential equations and study the integr...
متن کاملLarge time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
Abstract. We show a large time behavior result for class of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. We use a PDE approach to extend the convergence result proved by Namah and Roquejoffre (1999) in the scalar case. Our proof is based on new comparison, existence and regularity results for systems. An interpretation of the solution of the system in...
متن کاملSome Results on the Large Time Behavior of Weakly Coupled Systems of First-order Hamilton-jacobi Equations
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. The large time behavior for systems of Hamilton-Jacobi equations have been obtained by...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2016
ISSN: 0036-1410,1095-7154
DOI: 10.1137/15m1010841