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Math Help - Form of Semi Linear Linear PDE's

  1. #1
    Senior Member bugatti79's Avatar
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    Form of Semi Linear Linear PDE's

    Hi Folks,
    Semi Linear PDE

    A book book gives a linear first order PDE in the form

    a(x,y)u_x+b(x,y)u_y+c(x,y)u=f(x,y)

    My lectures notes has a 'semi linear' PDE in the form
    a(x,y)u_x+b(x,y)u_y=h(x,y,u)

    The presence of u on the RHS makes the PDE semi linear however where does the independant variable u itself disappear in the second equation?

    Thanks
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  2. #2
    Super Member Matt Westwood's Avatar
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    It hasn't disappeared. The first equation can be expressed in the form of the second by susbsituting:

    h(x, y, u) = f(x, y) - c(x, y) u

    In a semi-linear equation there is no constraint that the function "h" needs to be linear in u.
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  3. #3
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by Matt Westwood View Post
    It hasn't disappeared. The first equation can be expressed in the form of the second by susbsituting:

    h(x, y, u) = f(x, y) - c(x, y) u

    In a semi-linear equation there is no constraint that the function "h" needs to be linear in u.
    Ok, thanks for that! Cheers
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