370 citations · 370 across the 4 of their papers we have counts for
4 papers
Unbounded Viscosity Solutions of Hybrid Control Systems
Guy Barles, Sheetal Dharmatti, Mythily Ramaswamy
We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the sys…
Dirac concentrations in Lotka-Volterra parabolic PDEs
Benoit Perthame, Guy Barles
We consider parabolic partial differential equations of Lotka-Volterra type, with a non-local nonlinear term. This models, at the population level, the darwinian evolution of a pop…
Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
Guy Barles, Cyril Imbert
The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account…
Ergodic type problems and large time behaviour of unbounded solutions of Hamilton-Jacobi Equations
Guy Barles, Jean-Michel Roquejoffre
We study the large time behavior of Lipschitz continuous, possibly unbounded, viscosity solutions of Hamilton-Jacobi Equations in the whole space . The associated ergodic pro…