for the equation $u_x^2+u_y^2=u^2$ find the integral surfaces passing through the circle $x=cos(s)$ $y=sin(s)$ $z=1$
I'm a little confused about finding all characteristic strips. Usually we are given initial data, so can I assume the initial curve has the form Γ:(s,0,h(s))Γ:(s,0,h(s)), or does that not give all the characteristic strips?
I don't understand enveloped surfaces very well, so I have no geometric intuition for what I've written down so far, and I don't know how to compute the conoid solution or integral surface. Could someone help me with the general setup for this part?