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Evolutionary Equations

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Von Karman Evolution Equations

Part of the book series: Springer Monographs in Mathematics ((SMM))

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Abstract

This chapter provides preliminary material dealing with evolutionary abstract equations that serve as a prototype for von Karman evolutions discussed in subsequent chapters. Special attention is paid to the existence and uniqueness of solutions to nonlinear evolutionary equations. The methods used are based on monotone operator theory and their adaptation to nonmonotone problems. In what follows we provide a brief exposition of nonlinear semigroup theory and related concepts in maximal-monotone operator theory. We restrict our attention to single-valued operators, although many results stated below remain true in the multivalued setting.

We also state several results pertinent to linear plate equations in a form convenient for applications in subsequent chapters.

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Authors and Affiliations

  1. Department of Mechanics & Mathematics, Kharkov National University, 61077, Kharkov, Ukraine

    Igor Chueshov

  2. Department of Mathematics, University of Virginia, Charlottesville, Virginia, 22904, USA

    Irena Lasiecka

Authors
  1. Igor Chueshov
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  2. Irena Lasiecka
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Correspondence to Igor Chueshov .

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Chueshov, I., Lasiecka, I. (2010). Evolutionary Equations. In: Von Karman Evolution Equations. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87712-9_2

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