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# Boundary Conditions - Diff Eq

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I have a problem with a question on my final exam. I do not expect nor want any help just a simple yes or no will suffice. I am solving the classic wave equation using the Laplace Transform method extended to partial derivatives. Not a problem. The issue is I have never run across a boundary condition such as this:
u(0,t) = sin(2*PI*t), 0<t<1
= 0          , t>1

(Note: there is no u(L,t) boundary condition specified. The usual initial conditions are specified) I have seen limits, constants and functions for boundary conditions, but never a boundary condition such as this. So on to my question... has anyone ever seen a boundary condition like this? [smile] Check box: [ ] Yes [ ] No (*) Sense this is a take home final I checked the book for any boundary value problems similar to this.

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With "usual initial conditions" I assume you mean u(x,0) = f(x) and du(x,0)/dt = g(x) ?

If so, yes, the given boundary condition is a type of Dirichlet boundary condition (also known as boundary condition of first kind), defining u(0,t) = h(t)

So yes, I have seen them.

- M

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Quote:
 Original post by thebolt00With "usual initial conditions" I assume you mean u(x,0) = f(x) and du(x,0)/dt = g(x) ?

Yes, in this case, the initial displacement and velocity.

Quote:
 If so, yes, the given boundary condition is a type of Dirichlet boundary condition (also known as boundary condition of first kind), defining u(0,t) = h(t)So yes, I have seen them.- M

Thanks

btw... It always helps to RTFT. There is a sentence stating:

Look for a solution which decays to zero with increasing X for all time.
(so... u(x,t) -> 0 as x -> infinity )

I hate it when I reach burn out during finals.

[Edited by - smc on May 13, 2007 11:25:53 AM]