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  • Research Article
  • Open Access

Asymptotic Behavior of Solutions to Some Homogeneous Second-Order Evolution Equations of Monotone Type

Journal of Inequalities and Applications20072007:072931

https://doi.org/10.1155/2007/72931

  • Received: 7 November 2006
  • Accepted: 12 April 2007
  • Published:

Abstract

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 .

Keywords

  • Hilbert Space
  • Asymptotic Behavior
  • Evolution Equation
  • Convergence Theorem
  • Additional Assumption

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA
(2)
Department of Mathematics, Tarbiat Modares University, P.O. Box, 14115-175 Tehran, Iran

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