1. ## A PDE problem

Hi MHF members,

I have the following PDE, how ever I do not know much about PDEs.
I am more an ODE guy. I would be glad if you can give me directions and/or
references for attacking the following equation
$\frac{\partial^2u}{\partial t^2}=-c^2\frac{\partial^4 u}{\partial x^4}$
which represents the motion of an elastic bar of length $L$
with a fixed end at $0$ and the other one is free.
It reminds me the heat equation when I factor this into components as
$(D_t-icD_x^2)(D_t+icD_x^2)u=0$,
how ever the coefficients are complex valued.
I believe there should be another way.

2. ## Re: A PDE problem

I solved he homogeneous equation by means of separation of variables. But how can I write the boundary conditions to proceed to obtain the required solution?

3. ## Re: A PDE problem

unfortunately your pictures/Latex aren't rendering so it's impossible to see your problem.

4. ## Re: A PDE problem

Here is the OP's post with the equations fixed...

I have the following PDE, how ever I do not know much about PDEs.
I am more an ODE guy. I would be glad if you can give me directions and/or
references for attacking the following equation

$\displaystyle \frac{\partial^2u}{\partial t^2}=-c^2\frac{\partial^4 u}{\partial x^4}$

which represents the motion of an elastic bar of length $L$
with a fixed end at $0$ and the other one is free.
It reminds me the heat equation when I factor this into components as

$\displaystyle (D_t-icD_x^2)(D_t+icD_x^2)u=0$,

how ever the coefficients are complex valued.
I believe there should be another way.