370 citations · 951 across the 49 of their papers we have counts for
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math.AP2007
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…
math.AP2007★ 370 cited
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…
math.AP2007★ 35 cited
Global Existence Results and Uniqueness for Dislocation Equations
Guy Barles, Pierre Cardaliaguet, Olivier Ley +1
We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the…