Lecture Notes in Mathematics : Modeling and Mathematical Theory - Michael Ruzicka

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Lecture Notes in Mathematics

Modeling and Mathematical Theory

By: Michael Ruzicka

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Paperback | 12 December 2000

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196 Pages

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17.15 x 24.77 x 1.91

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This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Fluid Mechanics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Hydraulics & Pneumatics Mathematics Calculus & Mathematical Analysis

Differential Calculus & Equations Medicine Medicine in General Mechanical Engineering Applied Mathematics Thermodynamics & Heat

Introduction	p. vn
Contents	p. xv
Modeling of Electrorheological Fluids LI General Balance Laws	p. 1
Electrorheological Fluids	p. 9
Linear Models for the Stress Tensor T	p. 15
Compressible Electrorheological Fluids	p. 18
Incompressible Electrorheological Fluids	p. 20
Mechanically Incompressible but Electrically Compressible Electrorheological Fluids	p. 21
Shear Dependent Electrorheological Fluids	p. 24
Mathematical Framework	p. 39
Setting of the Problem and Introduction	p. 39
Function Spaces	p. 43
Maxwell's Equations	p. 54
Electrorheological Fluids with Shear Dependent Viscosities: Steady Flows	p. 61
Introduction	p. 61
Weak Solutions	p. 62
Strong Solutions	p. 71
Approximations	p. 74
Existence of Approximate Solutions	p. 84
Limiting Process A → oo	p. 93
Limiting Process ¿ → 0	p. 101
Electrorheological Fluids with Shear Dependent Viscosities: Unsteady Flows	p. 105
Setting of the Problem and Main Results	p. 105
Approximations	p. 110
Existence of Approximate Solutions	p. 114
Limiting Process A → ∞	p. 126
Limiting Process ¿ → 0	p. 142
Appendix	p. 153
General Auxiliary Results	p. 153
Auxiliary Results for the Approximations	p. 158
References	p. 165
Index	p. 175
Table of Contents provided by Publisher. All Rights Reserved.

Lecture Notes in Mathematics

Modeling and Mathematical Theory

At a Glance

Paperback

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How to return your order

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