Abstract
We consider nonlinear autonomous operator differential equations with pseudomonotone interaction functions satisfying \((S)\)-property. The dynamics of all weak solutions on the positive time semi-axis is studied. We prove the existence of a trajectory and a global attractor in a strongest topologies and study their structure. As a possible application, we consider the class of high-order nonlinear parabolic equations.
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Acknowledgments
This work was partially supported by the Ukrainian State Fund for Fundamental Researches under grants GP/F44/076, GP/F49/070, and by the NAS of Ukraine under grant 2273/13.
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Zgurovsky, M.Z., Kasyanov, P.O. (2014). Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies. In: Zgurovsky, M., Sadovnichiy, V. (eds) Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-03146-0_11
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DOI: https://doi.org/10.1007/978-3-319-03146-0_11
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