Archive for Rational Mechanics and Analysis

, Volume 122, Issue 2, pp 123–144

Phragmén-lindelöf type results for harmonic functions with nonlinear boundary conditions

  • C. O. Horgan
  • L. E. Payne
Article

DOI: 10.1007/BF00378164

Cite this article as:
Horgan, C.O. & Payne, L.E. Arch. Rational Mech. Anal. (1993) 122: 123. doi:10.1007/BF00378164

Abstract

This paper is concerned with investigating the asymptotic behavior of harmonic functions defined on a three-dimensional semi-infinite cylinder, where homogeneous nonlinear boundary conditions are imposed on the lateral surface of the cylinder. Such problems arise in the theory of steady-state heat conduction. The classical Phragmén-Lindelöf theorem states that harmonic functions which vanish on the lateral surface of the cylinder must either grow exponentially or decay exponentially with distance from the finite end of the cylinder. Here we show that the results are significantly different when the homogeneous Dirichlet boundary condition is replaced by the nonlinear heatloss or heat-gain type boundary condition. We show that polynomial growth (or decay) or exponential growth (or decay) may occur, depending on the form of the nonlinearity. Explicit estimates for the growth or decay rates are obtained.

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • C. O. Horgan
    • 1
    • 2
  • L. E. Payne
    • 1
    • 2
  1. 1.Department of Applied MathematicsUniversity of VirginiaCharlottesville
  2. 2.Department of MathematicsCornell UniversityIthaca