I have the PDE given by

\begin{align} \dfrac{\partial C}{\partial t}-\nabla\cdot(D\nabla C)+V\cdot\nabla C+RC&=\sum_{i=1}^{N}w_{i}(t)\delta(x-x_{i})\\ C(x,0)&=C_{0}(x)\\ C(0,t)&=C(t)\\ \nabla C(\ell,t)&=0 \end{align} I would like to show the uniqueness of the solututions using the energy methods. I read a book by Evans (page 63) where they showed uniqueness to the Heat equation. The problem is I dont know how to come up with the energy function inorder to use for the problem.


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