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This paper is concerned with radially symmetric solutions of systems of theform \[ u_t = -\nabla V(u) + \Delta_x u \] where space variable $x$ and andstate-parameter $u$ are multidimensional, and the potential $V$ is coercive atinfinity. For such systems, under generic assumptions on the potential, theasymptotic behaviour of solutions "stable at infinity", that is approaching aspatially homogeneous equilibrium when $|x|$ approaches $+\infty$, isinvestigated. It is proved that every such solutions approaches a stackedfamily of radially symmetric bistable fronts travelling to infinity. Thisbehaviour is similar to the one of bistable solutions for gradient systems inone unbounded spatial dimension, described in a companion paper. It is expected(but unfortunately not proved at this stage) that behind these travellingfronts the solution again behaves as in the one-dimensional case (that is, thetime derivative approaches zero and the solution approaches a pattern ofstationary solutions).

Global behaviour of radially symmetric solutions stable at infinity for gradient systems