Steady-state problems of nonlinear electro-magneto-thermo-elasticity
In this paper, steady state problems in nonlinear electro-magneto-thermo- elasticity are studied. In part I of the paper, the governing equations, constitutive equations, and boundary conditions are treated. Use is made of strong ellipticity condition in place of Clausius-Duhem inequality. Some general existence theorems in two cases, namely (i) conservative systems and (ii) rigid conductors are stated and proved. In part II, some semi-inverse problems are formulated for a cylindrical tube and the consequences of strong ellipticity and growth conditions are discussed. Existence of classical solutions to certain boundary-value problems when the strong ellipticity and growth conditions hold is proved. Methods and notations of functional analysis are used throughout the above discussions. The paper will be definitely of interest to those seeking the applications of functional analysis to physical problems.
nonlinear electro-magneto-thermo-elasticity
scientific article; zbMATH DE number 4031196
scientific article