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PDE - Characteristics

  1. Oct 1, 2015 #1
    1. The problem statement, all variables and given/known data
    1. ut +ux = 0 subject to u(t,x) = x on x^2 + y^2 = 1

      Is this a well-posed PDE BVP?

    2. Relevant equations


    3. The attempt at a solution
    This is an easy one to solve: u(t,x) = f(x-t)
    I let t(0) = 0 as an initial condition, and so t=s => x= ts + xo, where x(0) = xo
    s is the variable such that ∂(u(t(s), x(s))/∂s = 0
    If I let u(t,x) = x = f(x-t), would this not be well-posed since f must be a function of (x-t)?
     
  2. jcsd
  3. Oct 2, 2015 #2

    Geofleur

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    Science Advisor
    Gold Member

    In the problem setup, is the condition really ## x^2 + y^2 = 1 ##, or did you mean ## x^2 + t^2 = 1 ##?
     
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