The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen–Cahn equations

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Generalized Transition Waves and Their Properties (2010, background): “1) in R for usual types of nonlinearities f (combustion, bistable, Kolmogorov-Petrovsky-Piskunov type), see [3, 10, 17, 18, 21, 22, 31, 40, 41] for details.”
Periodic pyramidal traveling fronts of bistable reaction-diffusion equations with time-periodic nonlinearity (2012, background): “Taniguchi [46,47] further studied the existence, uniqueness and stability of three-dimensional pyramidal traveling fronts of (1.”
Periodic traveling curved fronts in reaction–diffusion equation with bistable time-periodic nonlinearity (2011, background): “Recently, the mathematical study on the nonplanar traveling wave solution is attracting a lot of attention, see [2,6–11,16,26,27] for more existence and stability results of nonplanar traveling wave solutions of the autonomous reaction–diffusion equation.”