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In this paper, the existence of solution for a \begin{document} $p$ \end{document} -Laplacian parabolic equation with nonlocal diffusion is established. To do this, we make use of a change of variable which transforms the original problem into a nonlocal one but with local diffusion. Since the uniqueness of solution is unknown, the asymptotic behaviour of the solutions is analysed in a multi-valued framework. Namely, the existence of the compact global attractor in \begin{document} $L^2(Ω)$ \end{document} is ensured.

Global attractor for a nonlocal <i>p</i>-Laplacian equation without uniqueness of solution