Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit
Benoît Perthame, Stephane Génieys (2010)
Mathematical Modelling of Natural Phenomena
Similarity:
The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing instability and the interpretation refers to adaptive evolution. By analogy with other formalisms used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum of Dirac masses) will happen in the limit of small mutations. In the present work we study this asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation. We prove the convergence...