Theorems on Existence and Uniqueness of the Generalised Solution for One-Dimensional Nonstationary Problems of Coupled Electroelasticity

Melnik (R.)V.N.

Modelling in Mechanics, 3(20), No.6, 70-77, 1989

Abstract:

In an earlier paper [same journal 3 (1989), no. 2, 124-133], we considered a mathematical model that describes a nonstationary process of coupled electroelastic oscillations of hollow infinite piezoceramic cylinders. Such problems arise in many applications where piezoelectric coupling is important (mechanical engineering, problems in electronics, etc). A difference scheme of second order of accuracy was constructed, a theorem on convergence and accuracy was proved, and computational experiments were carried out. Here we study in detail the well-posedness of the model and prove existence and uniqueness theorems for the generalized solution to the problem.