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For nonlinear parabolic gradient systems of the form \[ u_t = -\nabla V(u) +u_{xx} \,, \] where the spatial domain is the whole real line, the statevariable $u$ is multidimensional, and the potential function $V$ is coercive atinfinity, the following result is proved: for every critical point of $V$ whichis not a global minimum point, there exists a travelling front, either pushedor pulled, invading this critical point at a speed which is not smaller thanits linear spreading speed. By contrast with previous existence results of thesame kind, no further assumption is made (neither that the invaded criticalpoint is a non-degenerate local minimum point, nor other assumptions ensuringpushed invasion).

Existence of a pulled or pushed travelling front invading a critical point for parabolic gradient systems