Potential method in the linear theory of triple porosity thermoelasticity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Svanadze, Merab¹ 

[1] Ilia State Univ, Inst Fundamental & Interdisciplinary Math Res, K Cholokashvili Ave 3-5, GE-0162 Tbilisi, Georgia

关键词: Thermoelasticity;    Triple porosity;    Uniqueness and existence theorems;    Potential method;   

DOI  :  10.1016/j.jmaa.2017.12.022

来源: Elsevier

【 摘 要 】

In this paper the linear theory of triple porosity thermoelasticity is considered and the basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, Green's identities are obtained and the Sommerfeld-Kupradze type radiation conditions are established. The surface (single-layer and double-layer) and volume potentials are constructed and their basic properties are given. The BVPs are reduced to the always solvable singular integral equations for which Fredholm's theorems are valid. Finally, the existence and uniqueness theorems for classical solutions of the basic BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free