Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents (1st ed. 2023) (Lecture Notes in Mathematics #2329)
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- Synopsis
- 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.
- Copyright:
- 2023
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783031296703
- Related ISBNs:
- 9783031296697
- Publisher:
- Springer International Publishing
- Date of Addition:
- 11/22/23
- Copyrighted By:
- The Editor
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Technology, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.