Author	Bakhvalov, N. author
Title	Homogenisation: Averaging Processes in Periodic Media [electronic resource] : Mathematical Problems in the Mechanics of Composite Materials / by N. Bakhvalov, G. Panasenko
Imprint	Dordrecht : Springer Netherlands, 1989
Connect to	http://dx.doi.org/10.1007/978-94-009-2247-1
Descript	XXXVI, 366 p. online resource

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1. Formulation of Elementary Boundary Value Problems -- ยง1. The Concept of the Classical Formulation of a Boundary Value Problem for Equations with Discontinuous Coefficients -- ยง2. The Concept of Generalized Solution -- ยง3. Generalized Formulations of Problems for the Basic Equations of Mathematical Physics -- 2. The Concept of Asymptotic Expansion. A Model Example to Illustrate the Averaging Method -- ยง1. Asymptotic expansion. A Formal Asymptotic Solution -- ยง2. Asymptotic Expansion of a Solution of the Equation u = 1 + ?u3 -- ยง3. Asymptotic Expansion of a Solution of the Equation (K(x/?)u?)?= f(x) by the Averaging Method -- ยง4. Generalization of the Averaging Method in the Case of a Piecewise Smooth Coefficient -- ยง5. Averaging the System of Differential Equations -- 3. Averaging Processes in Layered Media -- ยง1. Problem of Small Longitudinal Vibrations of a Rod -- ยง2. Nonstationary Problem of Heat Conduction -- ยง3. Averaging Maxwell Equations -- ยง4. Averaging Equations of a Viscoelastic Medium -- ยง5. Media with Slowly Changing Geometric Characteristics -- ยง6. Heat Transfer Through a System of Screens -- ยง7. Averaging a Nonlinear Problem of the Elasticity Theory in an Inhomogeneous Rod -- ยง8. The System of Equations of Elasticity Theory in a Layered Medium -- ยง9. Considerations Permitting Reduction of Calculations in Constructing Averaged Equations -- ยง10. Nonstationary Nonlinear Problems -- ยง11. Averaging Equations with Rapidly Oscillating Nonperiodic Coefficients -- ยง12. Problems of Plasticity and Dynamics of Viscous Fluid as Described by Functions Depending on Fast Variables -- 4. Averaging Basic Equations of Mathematical Physics -- ยง1. Averaging Stationary Thermal Fields in a Composite -- ยง2. Asymptotic Expansion of Solution of the Stationary Heat Conduction Problem -- ยง3. Stationary Thermal Field in a Porous Medium -- ยง4. Averaging a Stationary System of Equations of Elasticity Theory in Composite and Porous Materials -- ยง5. Nonstationary Systems of Equations of Elasticity and Diffusion Theory -- ยง6. Averaging Nonstationary Nonlinear System of Equations of Elasticity Theory -- ยง7. Averaging Stokes and Navier-Stokes Equations. The Derivation of the Percolation Law for a Porous Medium (Darcyโs Law) -- ยง8. Averaging in case of Short-Wave Propagation -- ยง9. Averaging the Transition Equation for a Periodic Medium -- ยง10. Eigenvalue Problems -- 5. General Formal Averaging Procedure -- ยง1. Averaging Nonlinear Equations -- ยง2. Averaged Equations of Infinite Order for a Linear Periodic Medium and for the Equation of Moment Theory -- ยง3. A Method of Describing Multi-Dimensional Periodic Media that does not Involve Separating Fast and Slow Variables -- 6. Properties of Effective Coefficients. Relationship Among Local and Averaged Characteristics of a Solution -- ยง1. Maintaining the Properties of Convexity and Symmetry of the Minimized Functional in Averaging -- ยง2. On the Principle of Equivalent Homogeneity -- ยง3. The Symmetry Properties of Effective Coefficients and Reduction of Periodic Problems to Boundary Value Problems -- ยง4. Agreement Between Theoretically Predicted Values of Effective Coefficients and Those Determined by an Ideal Experiment -- 7. Composite Materials Containing High-Modulus Reinforcement -- ยง1. The Stationary Field in a Layered Material -- ยง2. Composite Materials with Grains for Reinforcement -- ยง3. Dissipation of Waves in Layered Media -- ยง4. High-Modulus 3D Composite Materials -- ยง5. The Splitting Principle for the Averaged Operator for 3D High-Modulus Composites -- 8. Averaging of Processes in Skeletal Structures -- ยง1. An Example of Averaging a Problem on the Simplest Framework -- ยง2. A Geometric Model of a Framework -- ยง3. The Splitting Principle for the Averaged Operator for a Periodic Framework -- ยง4. The Splitting Principle for the Averaged Operator for Trusses and Thin-walled Structures -- ยง5. On Refining the Splitting Principle for the Averaged Operator -- ยง6 Asymptotic Expansion of a Solution of a Linear Equation in Partial Derivatives for a Rectangular Framework -- ยง7 Skeletal Structures with Random Properties -- 9. Mathematics of Boundary-Layer Theory in Composite Materials -- ยง1. Problem on the Contact of Two Layered Media -- ยง2. The Boundary Layer for an Elliptic Equation Defined on a Half-Plane -- ยง3. The Boundary Layer Near the Interface of Two Periodic Structures -- ยง4. Problem on the Contact of Two Media Divided by a Thin Interlayer -- ยง5. The Boundary Layer for the Nonstationary System of Equations of Elasticity Theory -- ยง6. On the Ultimate Strength of a Composite -- ยง7. Boundary Conditions of Other Types -- ยง8. On the Averaging of Fields in Layer Media with Layers of Composite Materials -- ยง9. The Time Boundary Layer for the Cauchy Parabolic Problem -- Supplement: Existence and Uniqueness Theorems for the Problem on a Cell

1. Mathematics
2. Partial differential equations
3. Mathematical models
4. Mechanics
5. Mathematics
6. Partial Differential Equations
7. Mathematical Modeling and Industrial Mathematics
8. Mechanics