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!

Homework Help: Burgers Equation Question - cannot satisfy initial conditions

  1. Feb 21, 2014 #1
    Burgers Equation Question -- cannot satisfy initial conditions

    1. The problem statement, all variables and given/known data

    Use characteristics to solve [tex]u_t+uu_x=0[/tex] on half line x≥0 with [tex]u(x,0)=x^2[/tex]

    2. Relevant equations


    3. The attempt at a solution

    I think I have an issue with the initial condition. So solving via characteristics gives:

    [tex] \frac{dx}{dt}=u \Rightarrow x=ut+x_0 \Rightarrow u=f(x-ut)[/tex]. Then we plug in initial values and get:

    [tex]u(x,0)=f(x)=x^2 \Rightarrow u=(x-ut)^2 \Rightarrow u^2t^2-u(1+2xt)+x^2=0[/tex]

    Then by quadratic formula

    [tex] u=\dfrac{(1+2xt) \pm \sqrt{(1+2xt)^2+4x^2t^2}}{2t^2} [/tex]

    Now here I have a problem. So, in order to pic which sign solution to use, I need to use the initial condition. However, at t=0, I have an obvious problem. If anyone could offer help, or whether there is a typo in the problem, that would be much appreciated!
  2. jcsd
  3. Feb 22, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What is the limit as t→0+?
  4. Feb 22, 2014 #3

    Thank you for a quick reply! I just did the limit out and that resolved my issue. Thank you very much!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted