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I have to solve the following PDE $$\frac{1}{\alpha}\frac{\partial T}{\partial t}=\frac{\partial^{2}T}{\partial r^{2}}+\frac{1}{r}\frac{\partial T}{\partial r}-\beta\cdot T+f(r,t)+\gamma$$ where $$f(r,t)=t(r)\cdot\frac{\dot{e}(t)}{k}$$ with $$t(r)=\frac{1}{2}\cdot\tanh(10(r-r_{1})+1)$$ and $$\dot{e}(t)=-\zeta\cdot t+\eta$$

I was thinking about solving it using Fourier Transform. Is it the best way or there's another one?

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    $\begingroup$ I presume that $r \in [0,\infty)$, as I see the radial Laplacian. If this is the case you cannot do a Fourier transform immediately, unless you ensure $r \in \mathbb{R}$. I would try separation of variables first. $\endgroup$ Jul 3, 2020 at 13:33

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What kind of initial and boundary conditions do you have? I might try a Laplace transform in the $t$ variable, if this is for $t \ge 0$ with initial conditions at $t=0$.

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  • $\begingroup$ That's all I have. With no boundary conditions or something like that. $\endgroup$
    – mvfs314
    Jul 3, 2020 at 13:33

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