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

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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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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Keywords

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