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E-raamat: Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents

  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Mathematics 2329
  • Ilmumisaeg: 11-Aug-2023
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783031296703
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Pseudo-Monotone Operator Theory for Unsteady Problems with Variable ExponentsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Mathematics 2329
  • Ilmumisaeg: 11-Aug-2023
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783031296703
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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 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.

Arvustused

This book is essentially based on the authors 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 Moroanu, zbMATH 1526.35002, 2024)

- 1. Introduction. - 2. Preliminaries. - Part I Main Part. -
3. Variable
BochnerLebesgue Spaces. - 4. Solenoidal Variable BochnerLebesgue 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.
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