1. The problem statement, all variables and given/known data ut +ux = 0 subject to u(t,x) = x on x^2 + y^2 = 1 Is this a well-posed PDE BVP? 2. Relevant equations 3. The attempt at a solution This is an easy one to solve: u(t,x) = f(x-t) I let t(0) = 0 as an initial condition, and so t=s => x= ts + xo, where x(0) = xo s is the variable such that ∂(u(t(s), x(s))/∂s = 0 If I let u(t,x) = x = f(x-t), would this not be well-posed since f must be a function of (x-t)?