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

$\displaystyle

r_t +(rU)_x =tau([r_t+(rU)_x])_t + tau( (rU)_t + (rU^2 + p)_x )_x

$

$\displaystyle

(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

$

$\displaystyle

(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

$

$\displaystyle

+ tau( [U(rU^2 +(N+5) p)]_t + [rU^4 + (N+8)pU^2 +(N+5) pRT]_x )_x

$

I want to obtain:$\displaystyle r_t,U_t,p_t$ or $\displaystyle r_t,U_t,T_t$

Can anybody give me pointers where should I start?

Thanks

Pipa