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

Format:

Book

Author/Creator:

Kaltenbach, Alex, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2329.

Lecture notes in mathematics, 0075-8434 ; volume 2329

Language:

English

Subjects (All):

Monotone operators.

Navier-Stokes equations.

Operator theory.

Differential equations, Partial.

Nonlinear functional analysis.

Physical Description:

xiii, 355 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer [2023]

Summary:

"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.

Notes:

Includes bibliographical references (pages 347-355).

Current copyright fee: GBP19.00 42\0.

ISBN:

9783031296697

3031296699

OCLC:

1397088502

Publisher Number:

10.1007/9783031296703