Inequalities in Mechanics and Physics
1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semip...
Main Authors:  , 

Format:  eBook 
Language:  English 
Published: 
Berlin, Heidelberg
Springer Berlin Heidelberg
1976, 1976

Edition:  1st ed. 1976 
Series:  Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics

Subjects:  
Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 2. Flow in the Interior of a Reservoir. Formulation in the Form of a Variational Inequality
 3. Solution of the Variational Inequality, Characteristic for the Flow of a Bingham Fluid in the Interior of a Reservoir
 4. A Regularity Theorem in Two Dimensions
 5. Newtonian Fluids as Limits of Bingham Fluids
 6. Stationary Problems
 7. Exterior Problem
 8. Laminar Flow in a Cylindrical Pipe
 9. Interpretation of Inequalities with Multipliers
 10. Comments
 VII. Maxwell’s Equations. Antenna Problems
 1. Introduction
 2. The Laws of Electromagnetism
 3. Physical Problems to be Considered
 4. Discussion of Stable Media. First Theorem of Existence and Uniqueness
 5. Stable Media. Existence of “Strong” Solutions
 6. Stable Media. Strong Solutions in Sobolev Spaces
 7. Slotted Antennas. NonHomogeneous Problems
 8. Polarizable Media
 9. Stable Media as Limits of Polarizable Media
 10. Various Additions
 11. Comments
 Additional Bibliography and Comments
 1. Comments
 2. Bibliography
 I. Problems of SemiPermeable Media and of Temperature Control
 1. Review of Continuum Mechanics
 2. Problems of SemiPermeable Membranes and of Temperature Control
 3. Variational Formulation of Problems of Temperature Control and of SemiPermeable Walls
 4. Some Tools from Functional Analysis
 5. Solution of the Variational Inequalities of Evolution of Section 3
 6. Properties of Positivity and of Comparison of Solutions
 7. Stationary Problems
 8. Comments
 II. Problems of Heat Control
 1. Heat Control
 2. Variational Formulation of Control Problems
 3. Solution of the Problems of Instantaneous Control
 4. A Property of the Solution of the Problem of Instantaneous Control at a Thin Wall
 5. Partial Results for Delayed Control
 6. Comments
 III. Classical Problems and Problems with Friction in Elasticity and ViscoElasticity
 1. Introduction
 2. Classical Linear Elasticity
 3. Static Problems
 4. Dynamic Problems
 5. Linear Elasticity with Friction or Unilateral Constraints
 6. Linear ViscoElasticity. Material with Short Memory
 7. Linear ViscoElasticity. Material with Long Memory
 8. Comments
 IV. Unilateral Phenomena in the Theory of Flat Plates
 1. Introduction
 2. General Theory of Plates
 3. Problems to be Considered
 4. Stationary Unilateral Problems
 5. Unilateral Problems of Evolution
 6. Comments
 V. Introduction to Plasticity
 1. Introduction
 2. The Elastic Perfectly Plastic Case (PrandtlReuss Law) and the ElastoViscoPlastic Case
 3. Discussion of ElastoViscoPlastic, Dynamic and QuasiStatic Problems
 4. Discussion of Elastic Perfectly Plastic Problems
 5. Discussion of RigidViscoPlastic and Rigid Perfectly Plastic Problems
 6. Hencky’s Law. The Problem of ElastoPlastic Torsion
 7. Locking Material
 8.Comments
 VI. Rigid ViscoPlastic Bingham Fluid
 1. Introduction and Problems to be Considered