Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region

R. J. Knops, L. E. Payne

Research output: Contribution to journalArticle

Abstract

A first order differential inequality is derived for the cross-sectional energy flux of the solution to the equation of constant mean curvature defined on a three-dimensional prismatic cylinder of convex cross-section. Integration of the inequality yields estimates which are employed to prove for large values of the axial variable that the solution in measure either grows at least algebraically or decays at most exponentially to the lower dimensional cross-sectional solution. This result generalises that previously obtained by the authors for the corresponding two-dimensional problem. © 1996 Kluwer Academic Publishers.

Original languageEnglish
Pages (from-to)597-606
Number of pages10
JournalMeccanica
Volume31
Issue number5
Publication statusPublished - 1996

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Constant Mean Curvature
Differential Inequalities
Asymptotic Behavior of Solutions
Cross section
Decay
First-order
Three-dimensional
Generalise
Energy
Estimate

Keywords

  • Constant mean curvature equation
  • Phragmén-Lindelöf principle
  • Thermomechanics of continua

Cite this

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abstract = "A first order differential inequality is derived for the cross-sectional energy flux of the solution to the equation of constant mean curvature defined on a three-dimensional prismatic cylinder of convex cross-section. Integration of the inequality yields estimates which are employed to prove for large values of the axial variable that the solution in measure either grows at least algebraically or decays at most exponentially to the lower dimensional cross-sectional solution. This result generalises that previously obtained by the authors for the corresponding two-dimensional problem. {\circledC} 1996 Kluwer Academic Publishers.",
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Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region. / Knops, R. J.; Payne, L. E.

In: Meccanica, Vol. 31, No. 5, 1996, p. 597-606.

Research output: Contribution to journalArticle

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AU - Payne, L. E.

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