Abstract
We consider a sequence of superposition operators (Nemytskii operators) from the space of square-integrable functions on a line segment to a separable Hilbert space. Each term of the sequence is generated by a time-dependent family of maximal monotone operators in the Hilbert space. Under sufficiently general assumptions we show that every superposition operator is maximal monotone and study the \( G \)-convergence of the respective sequence of Nemytskii operators. The results can be used to study the parametric dependence of solutions to evolutionary inclusions with time-dependent maximal monotone operators.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 6, pp. 1369–1381. https://doi.org/10.33048/smzh.2022.63.615
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Tolstonogov, A.A. The \( G \)-Convergence of Maximal Monotone Nemytskii Operators. Sib Math J 63, 1169–1180 (2022). https://doi.org/10.1134/S0037446622060155
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DOI: https://doi.org/10.1134/S0037446622060155