SPATIAL DECAY-ESTIMATES FOR A COUPLED SYSTEM OF 2ND-ORDER QUASI-LINEAR PARTIAL-DIFFERENTIAL EQUATIONS ARISING IN THERMOELASTIC FINITE ANTIPLANE SHEAR

The spatial decay behavior of solutions of a coupled system of second- order quasilinear partial differential equations, in divergence form, defined on a two-dimensional semi-infinite strip, is investigated. Suc h equations arise in the theory of anti-plane shear deformations for i sotropic nonlinearly thermoelastic solids. Differential inequality tec hniques are employed to obtain exponential decay estimates. The result s are illustrated by several examples. The results are relevant to Sai nt-Venant principles for nonlinear thermoelasticity as well as to theo rems of Phragmen-Lindelof type.