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Minimal Surface and Boundary Equation

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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?

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Solution Summary

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

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

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.

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