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

Heat eqtn with Generation term

  1. Mar 22, 2010 #1
    Hey,

    I am wondering how to solve this heat equation with a 'generation' term included. In one instance I am adding the generation term, in the other I am subtracting it.

    [tex] a\frac{\partial^{2}f }{\partial x^{2}}-\frac{\partial f}{\partial t} - \lambda f = 0[/tex]

    [tex] a\frac{\partial^{2}f }{\partial x^{2}}-\frac{\partial f}{\partial t} + \lambda f = 0[/tex]


    Any information on how to solve these/links to a table would be great :D
     
  2. jcsd
  3. Mar 22, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Of course, you need some initial/boundary conditions to have a well posed problem. I would try separation of variables.
     
  4. Mar 23, 2010 #3
    Is the system bounded or is it in the whole space (x-axis in our case)?

    A problem with boundary condition would be best solved with variable separation.
    An infinite problem would be best solved with a Fourier Transform.

    Both will give you an implicit form solution (as a sum or an integral) unless the initial conditions are specifically chosen.
     
  5. Mar 23, 2010 #4
    Look at Partial Differential Equations: Sources and Solutions by AD Snider.

    He talks about how to solve these sorts of problems.
    I think the solution is to use a combination of Green's functions and Laplace transforms, but I do not recall exactly.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Heat eqtn with Generation term
Loading...