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Quasilinear pde

  1. Mar 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Solve the following IVP for 1st order quasilinear PDE
    s using the method of characteristics.

    u*u_x + y*u_y = x

    u = 2s, y = s, x = s

    2. Relevant equations

    a(x,y,z)*u_x + b(x,y,z)*u_y = c(x,y,z)

    z = u(x_o,y_o) = 2s

    3. The attempt at a solution

    The problem confuses me in the sense that this is the first one where x and y aren't coupled with their respective partial derivatives. for example I can solve

    x*u_x + y*u_y = x*u

    I'm just looking for more insight into the method of characteristics. does it imply that I can replace u with x with the parameters?

    back to the original problem

    u*u_x + y*u_y = x

    u = 2s, y = s, x = s

    is this an acceptable approach

    dx/dk = u

    and using the characteristic to write

    dx/dk = 2x (where s is the first parameter, and k the second one because the equation has 2 independent vars)

    dy/dk = y

    dz/dk = x

    this is the only part that confuses me and makes me believe im missing the bigger picture for this method.

  2. jcsd
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