Thread: Wave Equation and Stokes Theorem

1. Wave Equation and Stokes Theorem

Good Morning everyone, I am stuck on a question that I can't get started so thank you for any help you give.

Derive the solution of the inhomogeneous wave equation on the half line using Stokes' Theorem via integrating over the domain of dependence.

$\displaystyle u_{tt}= c^2u_{xx} + g(x,t)$
$\displaystyle u(x,0)=h(x), \ u(0,t)=\xi(x), \ u_t(x,0)=\phi(x)$, $\displaystyle 0<x<\infty$

2. Re: Wave Equation and Stokes Theorem

Well, where, exactly is your problem? Do you know what Stoke's theorem says? Do you know what the "domain of dependence" is?

3. Re: Wave Equation and Stokes Theorem

My problem is applying stokes theorem properly. I have an o.k understanding of stokes theorem and what is meant by 'domain of dependence', and I know the solution will be split into two, one for x>ct>0 and another for 0<x<ct. The domain of dependence will be involved in the solution via the part of the solution:

$\displaystyle \frac{1}{2c}\int_\triangle \int f$

But I don't really know how to get the rest of the solution. Thanks