Some theory for study the following system of pde...
$u_t = f(u,v) + d_1(u_{xx} + u_{yy})$
$v_t = g(u,v) + d_2(v_{xx} + v_{yy})$
where $u=u(x,y,t)$, $v = v(x,y,t)$, such that $(x,y,t)\in\mathbb{R}_{+,0}^{3}$ and $f,g\in C^0(\mathbb{R}_{+,0}^{2}) $
with different boundary conditions. (TThe system is a model for the predator-prey interaction)
Thanks friends!