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Asymptotic behavior of dynamical system governed by monotone operators and applications

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Abstract

To solve inclusion governed by maximal monotone operator, we consider the associated Cauchy problem with a parameter in Yosida approximate that depends on time. This allows us to generate trajectories that converge weakly, as t tends to infinity, to the solution of the inclusion problem. No additional assumptions are required for the operator. As a main application, we consider the non-autonomous continuous dynamical systems which are linked to Newton and Levenberg–Marquardt methods. The second application concerns the convex structured minimisation problems.

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  1. Faculty of Sciences Semlalia, Mathematics, Cadi Ayyad university, 40000, Marrakech, Morroco

    Zaki Chbani & Hassan Riahi

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  1. Zaki Chbani
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  2. Hassan Riahi
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Correspondence to Zaki Chbani.

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Chbani, Z., Riahi, H. Asymptotic behavior of dynamical system governed by monotone operators and applications. Afr. Mat. 26, 1593–1600 (2015). https://doi.org/10.1007/s13370-014-0311-6

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  • DOI: https://doi.org/10.1007/s13370-014-0311-6

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