Solving PDEs with IC, BCs: Help from Kevin

[jimmygriffey]

Hi:

I have the following PDE:

y_tzz=y_zzzz+delta(t)

With I.C.: t=0, y=0; and B.C.s: z=0, y=0,y_zz=0; z=-x,y=0,y_z=0

Can someone show me how to solve it?

Kevin

 

[Astronuc]

It the delta(t) actually δ(t)?

The problem looks remarkably similar to one's other problem - Help to solve 4th order ode.

 

[jimmygriffey]

Yes, it is δ(t). The one is very similar to the previous one. After taking Laplace transform in t, this one will become the previous one. If I use the method pointed by other people, I have hard time to convert back (inverse Laplace transform) to time domain. That's why I ask the question again.

Kevin

 

[Astronuc]

Yes, it is δ(t). The one is very similar to the previous one. After taking Laplace transform in t, this one will become the previous one. If I use the method pointed by other people, I have hard time to convert back (inverse Laplace transform) to time domain. That's why I ask the question again.

Kevin

Yes - if one uses the Laplace Transform (which takes an equation from time domain to frequncy domain) then I believe it is the same problem. I'm expecting the problem is separable, i.e. Y(z,t) = Z(z)T(t). See if that works.