*Accepted Paper*

**Inserted:** 11 mar 2011

**Last Updated:** 27 may 2012

**Journal:** Math. Models Methods Appl. Sci.

**Year:** 2011

**Abstract:**

We prove that solutions of a mildly regularized Perona-Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the general principle that ``the limit of gradient-flows is the gradient-flow of the limit''. To this end, we exploit a general result relating the Gamma-limit of a sequence of functionals to the limit of the corresponding maximal slope curves.

**Keywords:**
Gamma-convergence, Perona-Malik equation, gradient-flow, maximal slope curves

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