Some qualitative properties for the total variation flow

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The anisotropic total variation flow (2005, methodology): “Guided by the explicit solutions found in [ 7 ] for the Total Variation Flow, we look for a solution of the form u(t, x) = a(t).”
Active unsupervised texture segmentation on a diffusion based feature space (2003, background): “A rather critical issue is the good choice of the diffusivity function g. For the application to texture features total variation (TV) flow [23, 2 , 16] seems to suit very well, since it removes oscillations and leads to piecewise constant results.”
Total Variation Flow and Sign Fast Diffusion in one dimension (2011, background): “3 of [3] or Theorem 3 of [4] for the homogeneous Dirichlet problem on bounded domains.”
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing (2003, background): “Existence and uniqueness results for the above minimization problem can be found in [1], [10], [25], [3] (see also [4]).”
Edge-preserving and scale-dependent properties of total variation regularization (2003, background): “In [4], Andreu et al prove that the solution to (3) for sufficiently large α”
Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise (2012, background): “It turns out (see [2,3]) that η ∈ ∂φ(u) if and only if there is z ∈ L∞(O;RN ) such that η = −div z, |z|∞ 1, and ∫ O ηudξ = φ(u).”