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

Journal of Inequalities and Applications volume 2007, Article number: 072931 (2007) Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, 79968, USA

    Behzad Djafari Rouhani

  2. Department of Mathematics, Tarbiat Modares University, P.O. Box, 14115-175, Tehran, Iran

    Hadi Khatibzadeh

Authors
  1. Behzad Djafari Rouhani
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  2. Hadi Khatibzadeh
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Correspondence to Behzad Djafari Rouhani.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Rouhani, B.D., Khatibzadeh, H. Asymptotic Behavior of Solutions to Some Homogeneous Second-Order Evolution Equations of Monotone Type. J Inequal Appl 2007, 072931 (2007). https://doi.org/10.1155/2007/72931

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

Keywords

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