Geodesic
Existence, uniqueness and stability of traveling wavefronts for nonlocal dispersal equations with convolution type bistable nonlinearity
Electronic journal of differential equations, Tome 2015 (2015)
This article concerns the bistable traveling wavefronts of a nonlocal dispersal equation with convolution type bistable nonlinearity. Applying a homotopy method, we establish the existence of traveling wavefronts. If the wave speed does not vanish, i.e. $c\neq 0$, then the uniqueness (up to translation) and the globally asymptotical stability of traveling wavefronts are proved by the comparison principle and squeezing technique.
Classification : 35K57, 35R20, 92D25
Keywords: nonlocal dispersal, traveling wavefronts, bistable nonlinearity, continuation method, squeezing technique 
@article{EJDE_2015__2015__a53,
     author = {Zhang,  Guo-Bao and Ma,  Ruyun},
     title = {Existence, uniqueness and stability of traveling wavefronts for nonlocal dispersal equations with convolution type bistable nonlinearity},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1325.35252},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a53/}
}
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%J Electronic journal of differential equations
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%F EJDE_2015__2015__a53
Zhang,  Guo-Bao; Ma,  Ruyun. Existence, uniqueness and stability of traveling wavefronts for nonlocal dispersal equations with convolution type bistable nonlinearity. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a53/