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Homogenisation: Averaging Processes in Periodic Media : Mathematical Problems in the Mechanics of Composite Materials / by N.S. Bakhvalov, G. Panasenko
(Mathematics and its Applications, Soviet Series ; 36)

版	1st ed. 1989.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1989
本文言語	英語
大きさ	XXXVI, 366 p : online resource
著者標目	*Bakhvalov, N.S author Panasenko, G author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical models LCSH:Mechanics FREE:Differential Equations FREE:Mathematical Modeling and Industrial Mathematics FREE:Classical Mechanics
一般注記	1. Formulation of Elementary Boundary Value Problems -- §1. The Concept of the Classical Formulation of a Boundary Value Problem for Equations with Discontinuous Coefficients -- §2. The Concept of Generalized Solution -- §3. 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 -- §1. Asymptotic expansion. A Formal Asymptotic Solution -- §2. Asymptotic Expansion of a Solution of the Equation u = 1 + ?u3 -- §3. Asymptotic Expansion of a Solution of the Equation (K(x/?)u?)?= f(x) by the Averaging Method -- §4. Generalization of the Averaging Method in the Case of a Piecewise Smooth Coefficient -- §5. Averaging the System of Differential Equations -- 3. Averaging Processes in Layered Media -- §1. Problem of Small Longitudinal Vibrations of a Rod -- §2. Nonstationary Problem of Heat Conduction -- §3. Averaging Maxwell Equations -- §4. Averaging Equations of a Viscoelastic Medium -- §5. Media with Slowly Changing Geometric Characteristics -- §6. Heat Transfer Through a System of Screens -- §7. Averaging a Nonlinear Problem of the Elasticity Theory in an Inhomogeneous Rod -- §8. The System of Equations of Elasticity Theory in a Layered Medium -- §9. Considerations Permitting Reduction of Calculations in Constructing Averaged Equations -- §10. Nonstationary Nonlinear Problems -- §11. Averaging Equations with Rapidly Oscillating Nonperiodic Coefficients -- §12. Problems of Plasticity and Dynamics of Viscous Fluid as Described by Functions Depending on Fast Variables -- 4. Averaging Basic Equations of Mathematical Physics -- §1. Averaging Stationary Thermal Fields in a Composite -- §2. Asymptotic Expansion of Solution of the Stationary Heat ConductionProblem -- §3. Stationary Thermal Field in a Porous Medium -- §4. Averaging a Stationary System of Equations of Elasticity Theory in Composite and Porous Materials -- §5. Nonstationary Systems of Equations of Elasticity and Diffusion Theory -- §6. Averaging Nonstationary Nonlinear System of Equations of Elasticity Theory -- §7. Averaging Stokes and Navier-Stokes Equations. The Derivation of the Percolation Law for a Porous Medium (Darcy’s Law) -- §8. Averaging in case of Short-Wave Propagation -- §9. Averaging the Transition Equation for a Periodic Medium -- §10. Eigenvalue Problems -- 5. General Formal Averaging Procedure -- §1. Averaging Nonlinear Equations -- §2. Averaged Equations of Infinite Order for a Linear Periodic Medium and for the Equation of Moment Theory -- §3. 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 -- §1. Maintaining the Properties of Convexity and Symmetry of the Minimized Functional in Averaging -- §2. On the Principle of Equivalent Homogeneity -- §3. The Symmetry Properties of Effective Coefficients and Reduction of Periodic Problems to Boundary Value Problems -- §4. Agreement Between Theoretically Predicted Values of Effective Coefficients and Those Determined by an Ideal Experiment -- 7. Composite Materials Containing High-Modulus Reinforcement -- §1. The Stationary Field in a Layered Material -- §2. Composite Materials with Grains for Reinforcement -- §3. Dissipation of Waves in Layered Media -- §4. High-Modulus 3D Composite Materials -- §5. The Splitting Principle for the Averaged Operator for 3D High-Modulus Composites -- 8. Averaging of Processes in SkeletalStructures -- §1. An Example of Averaging a Problem on the Simplest Framework -- §2. A Geometric Model of a Framework -- §3. The Splitting Principle for the Averaged Operator for a Periodic Framework -- §4. The Splitting Principle for the Averaged Operator for Trusses and Thin-walled Structures -- §5. On Refining the Splitting Principle for the Averaged Operator -- §6 Asymptotic Expansion of a Solution of a Linear Equation in Partial Derivatives for a Rectangular Framework -- §7 Skeletal Structures with Random Properties -- 9. Mathematics of Boundary-Layer Theory in Composite Materials -- §1. Problem on the Contact of Two Layered Media -- §2. The Boundary Layer for an Elliptic Equation Defined on a Half-Plane -- §3. The Boundary Layer Near the Interface of Two Periodic Structures -- §4. Problem on the Contact of Two Media Divided by a Thin Interlayer -- §5. The Boundary Layer for the Nonstationary System of Equations of Elasticity Theory -- §6. On the Ultimate Strength of a Composite -- §7. Boundary Conditions of Other Types -- §8. On the Averaging of Fields in Layer Media with Layers of Composite Materials -- §9. The Time Boundary Layer for the Cauchy Parabolic Problem -- Supplement: Existence and Uniqueness Theorems for the Problem on a Cell 'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y semis point all,,: human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non­ The series is divergent: therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ !inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. 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