Evolutionary Equations

  • Igor Chueshov
  • Irena Lasiecka
Part of the Springer Monographs in Mathematics book series (SMM)


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.


Generalize Solution Weak Solution Evolutionary Equation Strong Solution Free Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media 2010

Authors and Affiliations

  1. 1.Department of Mechanics & MathematicsKharkov National UniversityKharkovUkraine
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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