Anisotropic solutions of a system of nonlinear parabolic equations (Q1873534)

The spatially anisotropic solutions of the system \[ \frac{\partial v_i}{\partial t} = \frac{\partial}{\partial x} \left(v^{-1}_i\frac{\partial v_i}{\partial x}\right) + \frac{\partial}{\partial y} \left(v^{-1}_i\frac{\partial v_i}{\partial y}\right) + f_i(v_1, v_2)\quad (i=1,2) \] are sought. Here \(f_i(\lambda v_1, \lambda v_2) = \lambda f_i(v_1, v_2)\).