Locally uniform convergence to an equilibrium for nonlinear parabolic equations on $R^N$

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Spreading and Vanishing for a Monostable Reaction–Diffusion Equation with Forced Speed (2018, methodology): “We then investigate the sharpness of the threshold from spreading to vanishing behaviours, in the same spirit as the results of [10, 11, 21, 23, 33] in the spatially homogeneous framework.”