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Some qualitative properties for the total variation flow

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Díaz Díaz, Jesús Ildefonso and Andreu, F. and Caselles, V. and Mazón, J.M. (2002) Some qualitative properties for the total variation flow. Journal of Functional Analysis, 188 (2). pp. 516-547. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123601938297


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:parabolic equations; support; spaces; total variation flow; nonlinear parabolic equations; asymptotic behaviour; eigenvalue type problem; propagation of the support
Subjects:Sciences > Mathematics > Differential equations
ID Code:15528
Deposited On:07 Jun 2012 07:53
Last Modified:12 Dec 2018 15:07

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