Convergence to steady states or periodic solutions in a class of Hamilton–Jacobi equations

By Jean-Michel Roquejoffre. 2001

107 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9712be0c2348c6048afde0d0294474a69cd5c580

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In Geometry and Topology

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints (2007, background): “As far as the author knows, only the periodic boundary condition and the Dirichlet boundary condition are treated for the large-time asymptotic problem in [4, 9–11, 21, 22] and in [1, 22], respectively.”
On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions (2011, unknown): “J.-M. Roquejoﬀre in [31] was also dealing with solutions of the Cauchy-Dirichlet problem which satisfy the Dirichlet boundary condition pointwise (in the classical sense) : this is a key diﬀerence with the results of [28, 29] where the solutions were satisfying the Dirichlet boundary condition in a…”
Ergodic Type Problems and Large Time Behaviour of Unbounded Solutions of Hamilton–Jacobi Equations (2006, background): “A different proof was given by Roquejoffre ( 2001 ).”
Long-time Behavior of Solutions of Hamilton–Jacobi Equations with Convex and Coercive Hamiltonians (2009, methodology): “We refer to the literatures [4, 6, 7, 10, 11, 21, 22, 23] and references therein for more details.”
Weak KAM Theorem in Lagrangian Dynamics (2001, result): “There now exists other proofs of the general case due to Barles-Souganidis and to Roquejoffre, see [BS00] and [Roq98b].”
Correctors for the homogenization of Hamilton‐Jacobi equations in the stationary ergodic setting (2003, background): “These applications range from front propagation in random media [5] to turbulentreaction diffusion equations and combustion [28], ergodic properties of controlled dynamical systems [1, 2], averaging behavior of Hamiltonian systems [16, 17], and the connection with the long-time asymptotics of Hamilt”
An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications (2013, methodology): “All these results (except perhaps the Namah–Roquejoffre ones) use in a crucial way the compactness of the domain: indeed either they are stated on a compact manifold or they use periodicity which means that we are looking at equations set on the torus.”
ASYMPTOTIC SOLUTIONS FOR LARGE-TIME OF HAMILTON-JACOBI EQUATIONS IN EUCLIDEAN $n$ SPACE(Viscosity Solution Theory of Differential Equations and its Developments) (2007, result): “We refer to [16], [26], [28], [6], [12] for previous results and developments.”