Pseudo-monotone operator theory for unsteady problems with variable exponents / Alex Kaltenbach.

Author
Kaltenbach, Alex [Browse]
Format
Book
Language
English
Published/​Created
  • Cham, Switzerland : Springer [2023]
  • ©2023
Description
xiii, 355 pages : illustrations ; 24 cm

Details

Subject(s)
Series
  • Lecture notes in mathematics (Springer-Verlag) ; 2329. [More in this series]
  • Lecture notes in mathematics, 0075-8434 ; volume 2329
Summary note
"This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents.This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier-Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner-Lebesgue spaces is not applicable. As a substitute for Bochner-Lebesgue spaces, variable Bochner-Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier-Stokes equations under general assumptions.Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject."-- provided by publisher.
Bibliographic references
Includes bibliographical references (pages 347-355).
Rights and reproductions note
Current copyright fee: GBP19.00 42\0.
ISBN
  • 9783031296697 ((paperback))
  • 3031296699 ((paperback))
OCLC
1397088502
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