Application of Abstract Differential Equations to Some Mechanical Problems

Abstract

- Preface. - Introduction. 1. Laplace problem in a strip. 2. Laplace problem in a sector. 3. Presentation of the different chapters. - 1: General notions, definitions and results. 1. Introduction. 2. General notions from functional analysis. 3. Vector-value functions of Banach spaces. 4. Semigroup of linear bounded operators in a Banach space. 5. Differential-operator equations and fold completeness. 6. Isomorphism and coerciveness. 7. Interpolation of spaces. 8. Useful theorems. - 2: Thermal conduction in a half-strip and a sector. 1. Asymptotic expansion for the thermal conduction in a plate. 2. Completeness of a system of root functions for the thermal conduction in a half-strip and a sector with smooth coefficients. 3. Completeness of a system of root functions for the thermal conduction in a half-strip with piecewise smooth coefficients. - 3: Elasticity problems in a half-strip. 1. Asymptotic expansion for the elasticity in a plate. 2. Completeness of a system of root functions for elasticity problems in a half-strip. 3. Thermoelasticity systems in bounded domains with non-smooth boundaries. - 4: Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite tube domains. 1. Abstract results for second order elliptic equations. 2. Boundary value problems for second order elliptic equations. 3. Boundary value problems for fourth order elliptic equations. - 5: Basis property of elementary solutions for second order elliptic equations with a selfadjoint operator coefficient. 1. Abstract results for second order elliptic equations with a selfadjoint operator coefficient. 2. Boundary value problems for second order elliptic equations. - Problems. References. List of notations. - Subject index. Author index.