### 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 language | English |
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Pages (from-to) | 597-606 |

Number of pages | 10 |

Journal | Meccanica |

Volume | 31 |

Issue number | 5 |

Publication status | Published - 1996 |

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### Keywords

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

### Cite this

*Meccanica*,

*31*(5), 597-606.

}

*Meccanica*, vol. 31, no. 5, pp. 597-606.

**Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region.** / Knops, R. J.; Payne, L. E.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic behaviour of solutions to the equation of constant mean curvature on a three-dimensional region

AU - Knops, R. J.

AU - Payne, L. E.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - Constant mean curvature equation

KW - Phragmén-Lindelöf principle

KW - Thermomechanics of continua

UR - http://www.scopus.com/inward/record.url?scp=0030262748&partnerID=8YFLogxK

M3 - Article

VL - 31

SP - 597

EP - 606

JO - Meccanica

JF - Meccanica

SN - 0025-6455

IS - 5

ER -