Alex Kaltenbach: Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents
Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents
Buch
- Springer International Publishing, 08/2023
- Einband: Kartoniert / Broschiert, Paperback
- Sprache: Englisch
- ISBN-13: 9783031296697
- Bestellnummer: 11568489
- Umfang: 372 Seiten
- Nummer der Auflage: 23001
- Auflage: 1st ed. 2023
- Gewicht: 563 g
- Maße: 235 x 155 mm
- Stärke: 21 mm
- Erscheinungstermin: 12.8.2023
- Serie: Lecture Notes in Mathematics - Band 2329
Achtung: Artikel ist nicht in deutscher Sprache!
Klappentext
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.