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: 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
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