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＜電子ブック＞
Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents / by Alex Kaltenbach
(Lecture Notes in Mathematics. ISSN:16179692 ; 2329)

版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XIII, 358 p. 11 illus. in color : online resource
著者標目	*Kaltenbach, Alex author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Fluid mechanics LCSH:Operator theory LCSH:Differential equations FREE:Functional Analysis FREE:Engineering Fluid Dynamics FREE:Operator Theory FREE:Differential Equations
一般注記	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 andnon-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 HTTP:URL=https://doi.org/10.1007/978-3-031-29670-3

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