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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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