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Operator Inclusions and Variation Inequalities in Infinite-Dimensional Spaces

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Evolution Inclusions and Variation Inequalities for Earth Data Processing I

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 24))

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Abstract

In this chapter we propose the general approach for studying mathematical models of stationary geophysical processes and fields of different nature. In the first section we study functional-topological properties of the resolving operator for operator inclusions with multi-valued weakly coercive maps of pseudo-monotone type. In the second section we investigate properties of solutions for parameterized operator problems with non-smooth, probably, discontinuous or multi-valued interaction functions. Further, we investigate variational inequalities in locally convex spaces. In Sect. 2.4 we develop the multi-valued penalty method for the investigation of stationary unilateral problems of non-linearized viscoelasticity theory. Further, we consider a general approach to the investigation of contact problems which can be described by equations of Hammerstein type, study operators equations with non-coercive maps, develop the method of simulated control with corresponding applications which demonstrate some advantages of the presented mathematical toolbar. The exposition is accompanied by classes of real mathematical models with different non-linear relationships between determinative parameters.

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Authors and Affiliations

  1. Inst. Applied System Analysis National Academy of Science, Nat. Techn. University Ukraine, 37, Peremogy Ave., 03056, Kyiv, Ukraine

    Dr. Mikhail Z. Zgurovsky, Valery S. Mel’nik & Pavlo O. Kasyanov

Authors
  1. Dr. Mikhail Z. Zgurovsky
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  2. Valery S. Mel’nik
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  3. Pavlo O. Kasyanov
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Correspondence to Mikhail Z. Zgurovsky .

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Zgurovsky, M.Z., Mel’nik, V.S., Kasyanov, P.O. (2011). Operator Inclusions and Variation Inequalities in Infinite-Dimensional Spaces. In: Evolution Inclusions and Variation Inequalities for Earth Data Processing I. Advances in Mechanics and Mathematics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13837-9_2

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