resolution of system of equation

[EDIT: 20110525 10:15 CDT - reformat - WDR]

good morning,

i have this system:

(dC/dt)+(dC/dz)+a*(d^2C/dz^2)+(dq/dt)=0

(dq/dt)=q-(b*C)

please how i can solve it?

thanks in advance.

Answer 1

[Walter Roberson]

It makes things easier for the reader when you are more specific about what variables a function is dependent upon.

A solution is as follows:

C(t, z) = _C1+_C2*exp((1+b)*t)
q(t) = -_C2*exp((1+b)*t)+b*_C1

Notice that once again your system is independent of z, which is most easily resolvable by making d2C/dz2 zero... but there are probably other solutions.

This is the third time that you have presented a pde that was effectively independent of one of its nominal derivatives. It would help you to learn to recognize and deal with those situations.