I need to normalice this Schnakegnber model in 2D:
$u_t=D_u(u_{xx}+u_{yy})-u+av+u^2v\\ v_t=D_u(u_{xx}+u_{yy})b-av-u^2v$
We also know that $a,b>0$.
Then I know that I'll applied separation of variables in order to apply superposition and find a solution. The BIG question is that, in most of internet articles, one can find the normalizacion of this model but in 1D.
How can I normalice this model in 2D? (as presented in the equations above)