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We consider a class of parabolic nonlocal 1-Laplacian equation align* uₜ+ (-) ˢ₁u=f in (0, T]. align* By employing the Rothe time-discretization method, we establish the existence and uniqueness of weak solutions to the equation above. In particular, different from the previous results on the local case, we infer that the weak solution maintains 12-H\"older continuity in time.
Li et al. (Thu,) studied this question.