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Long-time behavior for competition-diffusion systems via viscosity comparison
We study the singular limit of
competition-diffusion systems in population dynamics when the
initial distribution of the solution is not entirely in a domain
of attraction for the system. We prove comparison principles in
the viscosity sense for the solution and supersolutions to the
system. By using travelling wave solutions and the distance
function to interfaces, we construct a viscosity supersolution.
Finally we study the dynamics of interfaces and the long time
behavior of the solution for the systems with large reaction
rates.