ON THE ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF LINEAR 2ND-ORDER BOUNDARY-TYPE PROBLEMS ON A SEMIINFINITE STRIP

This paper treats the asymptotic behavior of solutions of a linear sec ond-order elliptic partial differential equation defined on a two-dime nsional semiinfinite strip. The equation has divergence form and varia ble coefficients. Such equations arise in the theory of steady-state h eat conduction for inhomogeneous anisotropic materials, as well as in the theory of anti-plane shear deformations for a linearized inhomogen eous anisotropic elastic solid. Solutions of such equations that vanis h on the long sides of the strip are shown to satisfy a theorem of Phr agmen-Lindelof type, providing estimates for the rate of growth or dec ay which are optimal for the case of constant coefficients. The result s are illustrated by several examples. The estimates obtained in this paper can be used to assess the influence of inhomogeneity and anisotr opy on the decay of end effects arising in connection with Saint-Venan t's principle.