- #1

Nicolaus

- 73

- 0

## Homework Statement

- ut +ux = 0 subject to u(t,x) = x on x^2 + y^2 = 1

Is this a well-posed PDE BVP?

## Homework Equations

## 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 + x

_{o}, where x(0) = x

_{o}

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)?