Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 72931, 8 pages
Asymptotic Behavior of Solutions to Some Homogeneous Second-Order Evolution Equations of Monotone Type
1Department of Mathematical Sciences, University of Texas at El Paso, El Paso 79968, TX, USA
2Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran
Received 7 November 2006; Accepted 12 April 2007
Academic Editor: Andrei Ronto
Copyright © 2007 Behzad Djafari Rouhani and Hadi Khatibzadeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the asymptotic behavior of solutions to the
second-order evolution equation a.e. , , where is a maximal monotone operator in a real Hilbert space with nonempty, and and are real-valued functions with appropriate conditions
that guarantee the existence of a solution. We prove a weak ergodic
theorem when is the subdifferential of a convex, proper, and lower
semicontinuous function. We also establish some weak and strong convergence
theorems for solutions to the above equation, under additional assumptions
on the operator or the function .