Results 1 to 4 of 4

Math Help - A PDE problem

  1. #1
    Senior Member bkarpuz's Avatar
    Joined
    Sep 2008
    From
    R
    Posts
    481
    Thanks
    2

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member bkarpuz's Avatar
    Joined
    Sep 2008
    From
    R
    Posts
    481
    Thanks
    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?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,653
    Thanks
    1063

    Re: A PDE problem

    unfortunately your pictures/Latex aren't rendering so it's impossible to see your problem.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,656
    Thanks
    1480

    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.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum