Convergence and sharp thresholds for propagation in nonlinear diffusion problems

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Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat (2014, unknown): “, [4, 18, 23, 24, 50, 56].”
Locally uniform convergence to an equilibrium for nonlinear parabolic equations on $R^N$ (2015, background): “2), several authors have addressed the asymptotic behavior of solutions with compact initial support, see [7, 8, 34] and references therein.”
Spreading and vanishing in nonlinear diffusion problems with free boundaries (2013, methodology): “Since f is of bistable type, it is well-known (see [9]) that bounded nonnegative solutions of (5.”
A diffusive logistic model with a free boundary in time-periodic environment☆ (2013, background): “However, in contrast to the above mentioned trichotomy of [15] in one space dimension with a bistable nonlinearity associated with the Cauchy problem, the free boundary model with a logistic type nonlinearity exhibits a spreading-vanishing dichotomy.”
Spreading and Vanishing for a Monostable Reaction–Diffusion Equation with Forced Speed (2018, methodology): “Proof This follows from a standard reflection method, as it is done for instance in [10].”