coefiecent of time dependent in pdepe solver

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Matt 2013-3-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/66392-coefiecent-of-time-dependent-in-pdepe-solver

Hello

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:

Any help?

Thanks