Ergodic Type Problems and Large Time Behaviour of Unbounded Solutions of Hamilton–Jacobi Equations
By Guy Barles, Jean-Michel Roquejoffre. 2006
55 citations recorded by the source corpus.
We study the large time behavior of Lipschitz continuous, possibly unbounded, viscosity solutions of Hamilton–Jacobi Equations in the whole space ℝ N . The associated ergodic problem has Lipschitz continuous solutions if the analogue of the ergodic constant is larger than a minimal value λmin. We obtain various large-time convergence and Liouville type theorems, some of them being of completely new type. We also provide examples showing that, in this unbounded framework, the ergodic behavior may fail, and that the asymptotic behavior may also be unstable with respect to the initial data.
Subfields: Applied Mathematics, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c4f2a8d07b259a073ee79e1b321dc436695b42ba
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Citations in the corpus
- Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints (2007, background): “More recently the large-time asymptotic problem of the same kind has been studied in the case when = Rn by Fujita-Ishii-Loreti [14], Barles-Roquejoffre [3], Ishii [16], and Ichihara-Ishii [15].”
- On the Large Time Behavior of Solutions of Hamilton–Jacobi Equations Associated with Nonlinear Boundary Conditions (2011, unknown): “Later, by using partially the ideas of [7] but also of [30], results on the asymptotic problem for unbounded solutions were provided in [6].”