Author | Titeux, Isabelle. author |
---|---|
Title | Application of Abstract Differential Equations to Some Mechanical Problems [electronic resource] / by Isabelle Titeux, Yakov Yakubov |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-94-007-1080-1 |
Descript | XXII, 209 p. online resource |
1. General notions, definitions, and results -- 1. Introduction -- 2. General notions from functional analysis -- 2.4 Dual spaces -- 3. Vector-valued functions in 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 in semi-infinite tube domains -- 1. Abstract results for second order elliptic equations with a selfadjoint operator coefficient -- 4. Boundary value problems for second order elliptic equations -- Problems -- References -- List of notations -- Author index