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math.AP2019★ 2 cited
Spreading speeds for multidimensional reaction-diffusion systems of the prey-predator type
Arnaud Ducrot, Thomas Giletti, Hiroshi Matano
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading prope…
math.AP2019★ 2 cited
Existence and uniqueness of propagating terraces
Thomas Giletti, Hiroshi Matano
This work focuses on dynamics arising from reaction-diffusion equations , where the profile of propagation is no longer characterized by a single front, but by a layer of several f…
math.AP2012★ 4 cited
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
Arnaud Ducrot, Thomas Giletti, Hiroshi Matano
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of so…