Consider the system
$$(I)\begin{cases} \frac{\partial u}{\partial t} = \nabla \cdot \left( D_1(x,t,u) \nabla u \right) + f_1(u,v) \\ \frac{\partial v}{\partial t} = \nabla \cdot \left( D_2(x,t,v)\nabla v \right) + f_2(u,v), \end{cases}$$
in $\Omega\times [0,T]$, with smooth initial data and Neumann boundary conditions.
First, I was interested on the existence and uniqueness of the solution of $(I)$. Then, I found a paper by Cannon J., Ford W, and Lair A, with title "Quiasilinear parabolic systems" avaible here. They deal with a nonlinear system of PDEs more general than $(I)$ and they establish conditions for existence and uniqueness of the solution (in the weak sense).
Then, I nocited they imposed some conditions on the diffusion coeffiencients, for example, the result (existence and uniqueness) is not valid if I consider $D_2 = 0$ (no diffusion means problems?). I didn't find any other referece covering this case. I understand that $D_2=0$ means that the second equation in $(I)$ is not parabolic anymore, and it is big change.
Is there any reference that includes the case $D_2=0$?