Artículo de revista
Strong asymptotic convergence of evolution equations governed by maximal monotone operators with Tikhonov regularization
Fecha
2008-12-15Registro en:
JOURNAL OF DIFFERENTIAL EQUATIONS Volume: 245 Issue: 12 Pages: 3753-3763 Published: DEC 15 2008
0022-0396
10.1016/j.jde.2008.08.007
Autor
Cominetti Cotti-Cometti, Roberto
Peypouquet, J.
Sorin, S.
Institución
Resumen
We consider the Tikhonov-like dynamics -(u) over dot(t) is an element of A(u(t)) + epsilon(t)u(t) where A is a maximal monotone operator on a Hilbert space and the parameter function epsilon(t) tends to 0 as t -> infinity with integral(infinity)(0)epsilon(t) dt = infinity. When A is the subdifferential of a closed proper convex function f, we establish strong convergence of u(t) towards the least-norm minimizer of f. In the general case we prove strong convergence towards the least-norm point in A(-1)(0) provided that the function epsilon(t) has bounded variation, and provide a counterexample when this property fails.