Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Very interesting problem

  1. Aug 17, 2010 #1
    I have spent hours and hours trying to solve a problem until reaching a dead point. I don't know how to solve, simplify, or proceed next with the following PDE:

    [tex]m \frac{\partial^2 x}{\partial t^2} + 2 \frac{\partial m}{\partial t} \frac{\partial x}{\partial t} + x \frac{\partial^2 m}{\partial t^2}=0[/tex]

    Or, in other words: mx_tt + 2m_tx_t + xm_tt = 0

    [tex]m x_{tt} + 2 m_{t} x_{t} + x m_{tt}[/tex]

    I thought it'd be easier but I don't seem to be able to simplify it. Maybe it is a form I don't recognize.

    JC
     
  2. jcsd
  3. Aug 17, 2010 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What are you trying to solve for? x and m are both unknown functions?
     
  4. Aug 17, 2010 #3
    Your equation can be written as:

    [tex]\frac{\partial ^2(m x)}{\partial t^2}=0[/tex]

    And this can be solved easily. Hope it helps you.
     
  5. Aug 18, 2010 #4
    Thanks.

    It helped me solve the differential equation, and it also made me realize that the solution is not what I expected it to be. I believe I need to revisit the formulation.

    Thanks again,

    JC
     
  6. Sep 5, 2010 #5
    You are welcome. Update us with your problem if you want.
     
  7. Sep 5, 2010 #6
    I've ended up with a variable coefficient wave equation, so I'm browsing for numerical solutions of similar problems at ScienceDirect.

    A closed form solution at this point is like asking Santa Claus for Dominion Over the Universe (yeah, um... not gonna happen).

    JC
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook