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Some Qualitative Properties for the Total Variation Flow

✍ Scribed by F. Andreu; V. Caselles; J.I. Dı́az; J.M. Mazón

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
427 KB
Volume
188
Category
Article
ISSN
0022-1236

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✦ Synopsis

We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations.

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