1. Limited time only! Sign up for a free 30min personal 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!

Diffusion equation

  1. Feb 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Hello, I don't understand the solution of an exercise

    Let P(x) be a continuous function such that |P(x)|≤Ceax² .
    Show that formula (8) for the solution of the diffusion equation makes sense for 0 < t < 1/(4ak), but not necessarily for larger t.

    2. Relevant equations
    Equation (8) refers to
    u(x,t)=1/√(4*pi*k*t) ∫ e-(x-y)²/4ktP(y) dy
    3. The attempt at a solution
    The solution just says that
    upload_2016-2-24_20-21-14.png

    I don't understand how they conclude ? I don't see why we have 0 < t < 1/(4ak)

    Thanks
     
  2. jcsd
  3. Feb 24, 2016 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Consider the sign of the ##y^2## term in the exponent. What has to be true for the integral to converge?
     
  4. Feb 25, 2016 #3
    I see, thanks !
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Diffusion equation
  1. Diffusion equation (Replies: 1)

  2. Diffusion Equation (Replies: 2)

  3. Diffusion equation (Replies: 6)

Loading...