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First order PDE with two conditions?

  1. Dec 7, 2011 #1
    Hello,

    I have a problem in the form

    [tex]\frac{\partial u}{\partial t}+\frac{\partial u}{\partial x}+e^{x}u=0[/tex]

    with conditions

    [tex]u(x,0)=u_0(x)[/tex]
    [tex]u(0,t)=\int_{0}^{\infty}f(x)u(x,t)dx[/tex]

    Im confused, because in first order PDE i require only 1 condition. How to solve this for two conditions?
     
  2. jcsd
  3. Dec 7, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You have only one condition- in each variable. Since this equation have the first derivative with respect to both x and t, you need one condition for each variable. If this were a "diffusion" (heat) equation, which involves the second derivative with respect to x and first derivative with respect to t, you need two conditions on x and on on t. If it were a "wave" equation, which involves the second order in both x and t, you would need two conditions on each variable.
     
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