Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents
indgår i Lecture Notes in Mathematics serien
- Indbinding:
- Paperback
- Sideantal:
- 372
- Udgivet:
- 12. August 2023
- Udgave:
- 23001
- Størrelse:
- 155x21x235 mm.
- Vægt:
- 563 g.
- 8-11 hverdage.
- 2. Oktober 2024
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Beskrivelse af 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 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.
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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