Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents

Alex Kaltenbach (Autor)

Buch | Softcover

XIII, 358 Seiten

2023 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-29669-7 (ISBN)

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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.

- 1. Introduction. - 2. Preliminaries. - Part I Main Part. - 3. Variable Bochner-Lebesgue Spaces. - 4. Solenoidal Variable Bochner-Lebesgue Spaces. - 5. Existence Theory for Lipschitz Domains. - Part II Extensions. - 6. Pressure Reconstruction. - 7. Existence Theory for Irregular Domains. - 8. Existence Theory for p- < 2. - 9. Appendix.

"This book is essentially based on the author's doctoral thesis ... . The book also contains an appendix and references. ... The book could be used by graduate students and researchers working on such problems." (Gheorghe Morosanu, zbMATH 1526.35002, 2024)

Erscheinungsdatum	13.08.2023
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIII, 358 p. 11 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	565 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Technik ► Maschinenbau
Schlagworte	Electrorheological Fluids • Existence of Weak Solutions • Pseudo-monotone Operator Theory • Variable Exponent Bochner-Lebesgue Spaces • variable exponent Lebesgue spaces • Variable Exponent Sobolev Spaces
ISBN-10	3-031-29669-9 / 3031296699
ISBN-13	978-3-031-29669-7 / 9783031296697
Zustand	Neuware