Suppose the PDE
$$u_t-\nabla(k((\vec{x})\nabla u)-q(\vec{x})u=F(\vec{x},t)\ \ ,\vec{x}\in\omega,\ \ \ t>0$$ with Neumann boundary condition $\nabla(\vec{x},t)\cdot\hat{n}=h(\vec{x},t), \ \ \ \vec{x}\in\partial\omega$. How do we prove that a solution to the problem is unique. Note that $k>0$ and $q<0$. Do we use the maximum principle, or the Duhamel principle here? Thanks beforehand.
