Wave equation with nonhomogenous neumann BC

[Mugged]

I've been searching online for the past week but can't seem to find what I am looking for.

I need the analytic solution to the wave equation: utt - c^2*uxx = 0

with neumann boundary conditions that are not homogeneous, i.e. ux(0,t) = A, for nonzero A.

also, the domain i require the solution to be in is a bounded domain (0 to L) or better yet the semi-infinite domain (0 to ∞)

can anyone refer me to a source?

Thank you

 

[lpetrich]

So it's u_tt - c²u_xx = 0
([noparse]u_tt - c²u_xx = 0[/noparse])

The general solution is easy: u = u1(x - c*t) + u2(x + c*t)
for arbitrary functions u1 and u2.
One can find it by changing variables to w1 = x - c*t and w2 = x + c*t

One can see from that solution that a single boundary condition won't be enough to fix u1 and u2. One will need two boundary conditions for that.

 

[Mugged]

I need more than the general solution

 

[Mute]

Have you tried solving it yourself?

 

[blue_raver22]

for your question. The wave equation with nonhomogeneous Neumann boundary conditions is a common problem in physics and engineering, and there are many sources available that provide solutions to this equation. One possible source is the book "Partial Differential Equations for Scientists and Engineers" by Stanley J. Farlow, which includes a section on the wave equation with nonhomogeneous boundary conditions. Another helpful resource is the website "MathWorld" by Eric W. Weisstein, which provides a detailed explanation and derivation of the solution to this equation. Additionally, you may want to consult with a colleague or mentor in your field who has experience with this type of problem and can provide guidance and references.