RT Journal Article
T1 Some qualitative properties for the total variation flow
A1 Díaz Díaz, Jesús Ildefonso
A1 Andreu, F.
A1 Caselles, V.
A1 Mazón, J.M.
AB 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.
PB Elsevier
SN 0022-1236
YR 2002
FD 2002-02-01
LK https://hdl.handle.net/20.500.14352/57328
UL https://hdl.handle.net/20.500.14352/57328
LA eng
NO DGCYT
NO TMR European Project "Viscosity Solutions and their Applications"
NO PNPGC
DS Docta Complutense
RD 6 abr 2025