I have the electrostatic equation like this ∇.(σ∇V)=∂ρ/∂t and if we write this in cylindrical coordinate it becomes: (1/r) *∂/∂r (rσ ∂V/∂r)=∂ρ/∂t and ρ is given by ρ=-(ε∇V ). So if u substitute the value of ρ it to the cylindrical equation: (1/r) *∂/∂r (rσ ∂V/∂r)=∂(-(ε∇V )/∂t.
Now my question is , is it possible to write (1/r) ∂/∂r (rσ ∂V/∂r)=∂(-(ε∇V )/∂t. it to diffusion form. I want the time dependence ∂(-(ε∇V )/∂t to be written [some value]∂V/∂t.
My aim is to solve (1/r) *∂/∂r (rσ ∂V/∂r)=∂(-(ε∇V )/∂t using pdepe solver: