Folks,

I am struggling to get the initial conditions @ t=0 for p and q.

Given $\displaystyle (u_x)^2+(u_y)^2-1=0$ for $\displaystyle u=0$ on $\displaystyle x^2+y^2=1$

My attempt:

Parameterise x such that $\displaystyle x=s$ and $\displaystyle y=\sqrt{1-s^2}$ and differentiate the given IC

$\displaystyle \displaystyle \frac{\partial u}{\partial x} \frac{d(s)}{ds}+\frac{\partial u}{\partial y} \frac{d(\sqrt{1-s^2})}{ds}=\frac{d(0)}{ds}$ This gives

$\displaystyle \displaystyle \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y} \frac{-s}{\sqrt{1-s^2}}=0$

Not sure if this right or how to proceed further to find pand q?

Thanks