1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help solving a PDE

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data

    The Cauchy problem for the advection-diffusion equation is given by:

    u.sub.t + c u.sub.x = K u.sub.xx (−∞< x < ∞)

    u(x, 0) = Phi(x)

    where c and K are positive constants.

    The advection-diffusion equation essentially combines the effects of the
    transport equation and the heat equation, so that the concentration profile
    is carried with speed c as it diffuses. The purpose of this problem is to
    solve the advection-diffusion equation using the following three steps:

    (1) Let v(x, t) = u(x + ct, t) and show that v(x, t) satisfies the heat equation,

    (2) Determine the initial condition that v(x, t) must satisfy; then, solve the
    resulting Cauchy problem for v(x, t).

    (3) Use the formula for v(x, t) from Step 2 to find u(x, t), the solution of the
    Cauchy problem for the advection-diffusion equation.

    THANK YOU SO VERY MUCH!!!


    2. Relevant equations

    See above.


    3. The attempt at a solution

    See https://www.physicsforums.com/showthread.php?t=588387
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Help solving a PDE
  1. PDE help (Replies: 0)

Loading...