Which of these equations is not parabolic?
(a) \(\rho\dot{q}\frac{\partial}{\partial x}(k\frac{\partial T}{\partial x})+\frac{\partial}{\partial y}(k\frac{\partial T}{\partial y})+\frac{\partial}{\partial z}(k\frac{\partial T}{\partial z})=\rho\frac{\partial e}{\partial t}\)
(b) \(\rho\dot{q}+\frac{\partial}{\partial x}(k\frac{\partial T}{\partial x})=\rho\frac{\partial e}{\partial t}\)
(c) \(\frac{1}{\rho C_v}[\frac{\partial}{\partial x}(k\frac{\partial T}{\partial x})+\frac{\partial}{\partial y}(k \frac{\partial T}{\partial y})+\frac{\partial}{\partial z}(k\frac{\partial T}{\partial z})]=\frac{\partial T}{\partial t} \)
(d) \(\frac{\partial}{\partial x}(k\frac{\partial T}{\partial x})+\frac{\partial}{\partial y}(k \frac{\partial T}{\partial y})+\frac{\partial}{\partial z}(k\frac{\partial T}{\partial z})=0\)
This question was addressed to me in homework.
My question is based upon Mathematical Behaviour of PDE in section Mathematical Behaviour of Partial Differential Equations of Computational Fluid Dynamics