Corner defects in almost planar interface propagation

By M. Haragus, Arnd Scheel. 2006

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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.”
Existence and qualitative properties of multidimensional conical bistable fronts (2005, background): “For every λ ∈ (0, 1) the function u satisfies (1.10) lim sup A→+∞, y≥A+φλ(x) |u(x, y)− 1| = 0, lim sup A→−∞, y≤A+φλ(x) |u(x, y)| = 0 Furthermore, all functions φλ have the same Lipschitz norm, say cotα with α ∈ (0, π/2], x̂ · ∇φλ(x) → − cotα as |x| → +∞, and c = c0/ sinα.”
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.”