hi,

i need to find non trivial conditions, for which the following system is well posed.

and then prove it is well posed.

$\displaystyle

u_{t}=\imath [A_{1}u_{xx} + A_{2}u_{yy}] \ + \ B_{1}u_{x}+B_{2}u_{y} \ +\ Cu \ +\ F \

$

$\displaystyle

u(t=0,x)=f(x);\ f(x)=f(x+2\pi) \

$

$\displaystyle

u\in C^N; \ A_j,B_j,C_j\in C^N; \ A_j=A_j^*; \ j=1,2

$