Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents / Lecture Notes in Mathematics Bd.2329 (PDF)
(Sprache: Englisch)
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...
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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.
Bibliographische Angaben
- Autor: Alex Kaltenbach
- 2023, 1st ed. 2023, 358 Seiten, Englisch
- Verlag: Springer International Publishing
- ISBN-10: 3031296702
- ISBN-13: 9783031296703
- Erscheinungsdatum: 11.08.2023
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- Grösse: 11 MB
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Englisch
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