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Math Help - PDE questions relating to Burgers equation and Power series

  1. #1
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    PDE questions relating to Burgers equation and Power series

    Hello, I am preparing for my PDE final, and I have questions relating to two problems:

    Solve the initial value problem for u = u(x,t)

    U_t + UU_x = 0

    -inf < x < inf for t > 0 and u(x,0) = tanh x for -inf < x < inf
    My usual approach to solving PDE problems in our course (like the heat and wave equation) has been to separate the variables and then look for common solutions. However, this doesn't appear to work here. How do I approach a problem like this? I see that it's an inviscid form of burger's equation, but I can't understand how to solve that.

    And for the second question:

    Find a series solution to the boundary value problem

    U_xx + U_yy = 0, 0 < x < 1, 0 < y < 4

    U_y(x,0) = f(x), U_y(x,4) = 0, 0 < x < 1

    U_x(0,y) = 0, U_x(1,y) = 0, 0 < y < 4
    For this problem, I'm able to separate the variables, but I am unsure how to form a power series solution to this problem. Thank you for any help you can provide!
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  2. #2
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    Re: PDE questions relating to Burgers equation and Power series

    For the first problem, use the method of characteristics. For the second, where did it say to find a power series. It just says series and I believe that a Fourier series will do that.
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