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Pseudo-monotone operator theory for unsteady problems with variable exponents

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Pseudo-monotone operator theory for unsteady problems with variable exponents/ by Alex Kaltenbach.
Author:	Kaltenbach, Alex.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xiii, 358 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Monotone operators. -
Online resource:	https://doi.org/10.1007/978-3-031-29670-3
ISBN:	9783031296703

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

Pseudo-monotone operator theory for unsteady problems with variable exponents[electronic resource] /by Alex Kaltenbach. - Cham :Springer International Publishing :2023. - xiii, 358 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23291617-9692 ;. - Lecture notes in mathematics ;1943..

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.

ISBN: 9783031296703

Standard No.: 10.1007/978-3-031-29670-3doiSubjects--Topical Terms:

672573
Monotone operators.

LC Class. No.: QA329.8 / .K35 2023

Dewey Class. No.: 515.724

Pseudo-monotone operator theory for unsteady problems with variable exponents
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520 $a 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.
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