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Confused about the terminology for the domain pde

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data

    δu/δt+2tδu/δx=1

    for t>0,x>0 with u= 0 on x= 0 for t>0, u=1 at t=0 for x≥0

    2. Relevant equations



    3. The attempt at a solution
    ((dx)/(dt))=2t
    x=t²+c
    x-t²=c
    the general solution is:
    u=t+F(x-t²)
    Now i am confused about the terminology for the domain, ie it says it is defined for t>0, x>0
    I am confused about u= 0 on x= 0 for t>0
    0=t+F(-t²)
    thus it follows that u(x,t)=t-√(t²+x)
    "at" x=o
    But what does it mean when is states this is only for t>0. For all t>0 when x is zero u will be zero anyway.
    The answer shows that the funcrtion u is equal to what i have solved for t²>x,
    and i can see that in this case the square root is defined(ie not √-)
    Then from the second condition the solution shows that u=1+t for t²≤x
    I would basically like to understand all this properly as i always get a bit confused with inequalities. How did they apply the second condition and inequality to get the second function and what was the reasoning?
     
  2. jcsd
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