Explore BrainMass
Share

Minimal Surface and Boundary Equation

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problems.

Show that
Z(x, y) = ln(sin y/sin x)

is a solution to the minimal surface equation.
(1 + Z)Z1 + 2ZXZZX + (1 + Z)Z = 0,
in the region 0 < x < ir, 0 < y < pi. What happens on the boundary of this region? Suppose we consider a constant multiple of Z(x, y) ? is it still a solution of the PDE?

© BrainMass Inc. brainmass.com October 24, 2018, 5:53 pm ad1c9bdddf
https://brainmass.com/math/numerical-analysis/minimal-surface-boundary-equation-23975

Attachments

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

(1)
...

Solution Summary

A minimum surface equation is investigated. The solution is detailed and well-presented.

$2.19
See Also This Related BrainMass Solution

Laminar Boundary Layer Flow Problem

Text Book : Viscous Fluid Flow by Tasos C. Papanastasiou
Download link for the book
http://www.filefactory.com/file/ag2609b/n/Viscous_Fluid_Flow_zip
http://www.filefactory.com/file/ag261a0/n/chapter08_pdf

Problem (8.1)
8.1. Water approaches an infinitely long and thin plate with uniform velocity.
(a) Determine the velocity distribution ux in the boundary layer given that
ux(x, y) = a(x)y² + b(x)y + c(x) .
(b) What is the flux of mass (per unit length of plate) across the boundary layer?
(c) Calculate the magnitude and the direction of the force needed to keep the plate in place.

View Full Posting Details