Mathematical problems of interaction of different dimensional physical fields

International Symposium on Dynamic Deformation and Fracture of Advanced Materials 2013

物理学;材料科学

Chkadua, G.^1

King's College London, Department of Mathematics, Strand, London WC2R 2LS, United Kingdom^1

关键词: Acoustic interaction;    Complex composite structures;    Existence theorem;    Mathematical problems;    Pseudodifferential equations;    Second-order partial differential equation;    Transmission conditions;    Transmission problem;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/451/1/012025/pdf
DOI  :  10.1088/1742-6596/451/1/012025

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

In the paper we consider mathematical problem of interaction of different dimensional physical fields for complex composite structures. We investigate the mixed transmission problem arising in the model of fluid-solid acoustic interaction when a piezo-ceramic elastic body (Ω+) is embedded in an unbounded fluid (Ω-). The corresponding physical process is described by boundary-transmission problems for second order partial differential equations. In particular, in the bounded domain Ω+we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain Ω-we have a scalar Helmholtz equation describing an acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations the uniqueness and existence theorems are proved in Sobolev-Slobodetski spaces.