Wave Equation and Stokes Theorem

**wallflower321** · October 7th 2011, 03:26 AM

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.

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

Can anyone help me please. Thank You for your help.

**HallsofIvy** · October 7th 2011, 11:01 AM

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

**wallflower321** · October 8th 2011, 01:05 AM

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:

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

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

Thread: Wave Equation and Stokes Theorem

LinkBack

Thread Tools

Display

Wave Equation and Stokes Theorem

Re: Wave Equation and Stokes Theorem

Re: Wave Equation and Stokes Theorem

Similar Math Help Forum Discussions

Stokes Theorem

Stokes Theorem

Surface Integrals, Stokes Theorem, Divergence Theorem, all the same?

Vector Calculus: Divergence theorem and Stokes' theorem

Using Stokes theorem

Search Tags