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Math Help - advection equation

  1. #1
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    advection equation

    Hi every body
    i wanna to find the solution of the advection equation u(x,t)with the following intial and boundary condtion.
    can it be solved by variable seperation
    \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial t}=0
    u(x,0)=sin(kx) intial condition
    u(0,t)=sin(wt) boundary condition
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  2. #2
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    Quote Originally Posted by amazing View Post
    Hi every body
    i wanna to find the solution of the advection equation u(x,t)with the following intial and boundary condtion.
    can it be solved by variable seperation
    \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial t}=0
    u(x,0)=sin(kx) intial condition
    u(0,t)=sin(wt) boundary condition
    I think probably what you meant is

    \dfrac {\partial u}{\partial t}+c\dfrac {\partial u}{\partial x}=0

    The solution does admit separation of variables but won't work with your IC and BC. The solution however is

     <br />
u = f(x-ct)<br />

    now use your IC/BC.
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  3. #3
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    thanks for your replay
    i know a bout the charactertics solution f(x-ct)
    but i wanna a solution that show the effect of bounday condition feeding on the solution.i mean a solution that is made by the IC/BC assumption
    not just to supsitute into the f(x-ct)
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