Application of Abstract Differential Equations to Some Mechanical Problems
By: by Isabelle Titeux, Yakov Yakubov
Contributors: Yakubov, Yakov
Series: Mathematics and Its Applications -- 558; Mathematics and Its Applications -- 558
Publisher: Springer Netherlands
Published: 2003
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 209
ISBN-13: 9789401037846; 9789400710801
Subjects: Differential Equations; Mechanics; Differential equations, partial; Materials; Mathematics; Operator theory
Description: The theory of differential operator equations has been described in various monographs. But the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained In this book, we give a systematic treatment of the differential equations with application to partial differential equations obtained from elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. We approximate and, when it is possible, expand the solution of problems by elementary solutions. This book is intended for scientists (mathematicians in the field of ordinary and partial differential equations, differential-operator equations; theoretical mechanics; theoretical physicists) and graduate students in Functional Analysis, Differential Equations, Equations of Mathematical Physics, and related topics.
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Table of contents: title: Preface; title: Introduction. 1; title: 1: General notions, definitions and results; title: 2: Thermal conduction in a half-strip and a sector; title: 3: Elasticity problems in a half-strip; title: 4: Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite tube domains; title: 5: Basis property of elementary solutions for second order elliptic equations with a selfadjoint operator coefficient; title: Subject index; title: Author index.