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Math Help - Tedious PDEs PRoblem

  1. #1
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    Tedious PDEs PRoblem

    I have 3 2nd order PDEs and I want to obtain 3 1st order PDEs from them. Following are the equations:

    <br />
r_t +(rU)_x =tau([r_t+(rU)_x])_t + tau(  (rU)_t  + (rU^2 + p)_x    )_x<br />

    <br />
 (rU)_t  + (rU^2 + p)_x   =  tau( (rU)_t  + (rU^2 + p)_x )_t  + tau(  (rU^2 + p)_t  +  [U(rU^2 +3 p)]_x )_x<br />

    <br />
(rU^2 +(N+3) p)_t  +  [U(rU^2 +(N+5) p)]_x = tau(  (rU^2 +(N+3) p)_t  +  [U(rU^2 +(N+5) p)]_x  )_t <br />
    <br />
 + tau(        [U(rU^2 +(N+5) p)]_t       +    [rU^4 + (N+8)pU^2 +(N+5) pRT]_x   )_x<br />

    I want to obtain: r_t,U_t,p_t or r_t,U_t,T_t

    Can anybody give me pointers where should I start?

    Thanks
    Pipa
    Last edited by pipa; April 4th 2009 at 10:15 AM. Reason: corrected first equation
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  2. #2
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    Is \tau a constant? Also, is there a relation between p\; \text{and}\; T. What's N, and integer 0, 1 or 2? Also, is there a derivative missing in the second term, first equations?
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  3. #3
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    Thanks for pointing that out. "Tau" is not a constant but can be treated like a constant for simplicity. The unit of Tau is time. N is just an integer and can be treated like a constant. P and T are related as follows:
    <br />
p=rRT<br />

    Thanks a lot for your reply!

    P.S. I corrected the first equation above
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