On the Capillary Surface in a Wide Circular Tube | Zendy

Erich Miersemann | Zendy

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On the Capillary Surface in a Wide Circular Tube

Author(s) -

Erich Miersemann

Publication year - 1997

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/755

Subject(s) - remainder , tube (container) , surface (topology) , capillary action , mathematics , radius , boundary (topology) , plane (geometry) , mathematical analysis , geometry , linearity , boundary value problem , physics , materials science , computer science , thermodynamics , arithmetic , computer security , quantum mechanics , composite material

An explicit asymptotic formula for the wide circular tube is proved. The leading term defines the capillary surface over the half plane with the given boundary contact angle. An explicit estimate of the remainder uniform with respect to the boundary contact angle and the radius of the tube is given. This uniform behaviour is caused by the strong non-linearity of the problem and has no counterpart for linear problems. The proof of the main result is based on a maximum principle and on a mapping which brings the right parameter of development onto the right place of the equation.

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