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: Answer need checking!

  1. Apr 28, 2006 #1
    I think I've solved this problem, but just need someone to check my answers.

    [tex]u_{x}u+u_{t}=2[/tex]

    With initial data

    [tex]u(x,0)=f(x)[/tex]

    Use the method of charactersitics [tex]u(x,t)=u(\xi,\tau)[/tex], we get

    [tex]\tau_{t}=t[/tex], [tex]x_{u}=u[/tex] and [tex]u_{\tau}=2[/tex].

    So, by choice of our initial condition,

    [tex]\tau=t[/tex] and [tex]u=2t + f(\xi)[/tex].

    Since [tex]\xi=\xi(x,t)[/tex]. We have

    [tex]u(x,t)=u(\xi(x,t),t)[/tex]

    At [tex]t=0[/tex] we have [tex]u(x,0)=u(\xi(x,0),0)[/tex], therefore

    [tex]x=\xi(x,0)[/tex]

    Since we do not know what [tex]f(x)[/tex] is, our solution for [tex]u(x,t)[/tex] is just

    [tex]u(x,t)=2t+f(\xi(x,t))[/tex]

    with initial condition

    [tex]\xi(x,0)=x[/tex]

    Is this right??
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted