consider this equation:
$$\frac {∂^2 T}{∂r^2 }+ \frac 1r \frac {∂T}{∂r}+ \frac 1{r^2} \frac {∂^2 T}{∂θ^2}+k v (\cos(θ) \frac{∂T}{∂r} -\frac 1r\sin(θ))-k \frac{∂T}{∂t}=0$$
within this boundary condition:
$$T(r,\theta,0)=0$$ $$\dfrac{\partial T}{\partial r} = - \dfrac{q}{2 \pi r \lambda }$$
I think about separational variable and green's function to solve the above equation , but I have a problem 4th term (last term) of the left hand side of my equation.
Could you please help me how can I dealing with this problem? (Any suggestions)
Thanks, Sanaz