Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents
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...
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| Ձևաչափ: | Էլեկտրոնային էլ․ գիրք |
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Cham :
Springer International Publishing : Imprint: Springer,
2023.
|
| Հրատարակություն: | 1st ed. 2023. |
| Շարք: | Lecture Notes in Mathematics,
2329 |
| Խորագրեր: | |
| Առցանց հասանելիություն: | https://doi.org/10.1007/978-3-031-29670-3 |
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| 100 | 1 | |a Kaltenbach, Alex. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents |h [electronic resource] / |c by Alex Kaltenbach. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a 1 online resource (XIII, 358 p. 11 illus.). |b 11 illus. in color. | ||
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2329 | |
| 520 | |a 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. | ||
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| 588 | |a Print version record. | ||
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Fluid mechanics. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 1 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Engineering Fluid Dynamics. |
| 650 | 2 | 4 | |a Operator Theory. |
| 650 | 2 | 4 | |a Differential Equations. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031296697 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031296710 |
| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2329 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-29670-3 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||