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Abstract Parabolic Evolution Equations and Their Applications by Atsushi Yagi

Abstract Parabolic Evolution Equations and Their Applications

by Atsushi Yagi
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Book cover type: Hardcover
  • ISBN13: 9783642046308
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 581
  • Original Price: USD 129.99
  • Language: English
  • Edition: 2010
  • Item Weight: 1012 grams
  • BISAC Subject(s): Differential Equations / General

This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0

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