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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| Korporativní autor: | |
| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Vydání: | 1st ed. 2023. |
| Edice: | Lecture Notes in Mathematics,
2329 |
| Témata: | |
| On-line přístup: | https://doi.org/10.1007/978-3-031-29670-3 |
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| Shrnutí: | 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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| Fyzický popis: | 1 online resource (XIII, 358 p. 11 illus.). 11 illus. in color. |
| ISBN: | 9783031296703 |
| ISSN: | 1617-9692 ; |
| DOI: | 10.1007/978-3-031-29670-3 |