Im having a really hard time with this question, I honestly don't even know how to start this...can anyone help me?
We are in the Parabolic section of PDE, and we are asked to find the unique solution of the following PDE (looks non-homogenous)
Problem: Let $\Omega$ be a bounded, normal domain in Rn. Assume a solution exists to the following PDE in some space. Prove the solution is unique, and State the conditions you need on the solutions in order to conclude uniqueness.
1: (Heat Equation w/ damping)
\begin{align} u_t = \nabla^2 u − u + F(x,t) \qquad & x \in \Omega, t > 0 \\ (∇u) \cdot \mathbf n = 0 \qquad & x\in \partial \Omega, t > 0 \\ u(x, 0) = f(x) \qquad & x \in \Omega \end{align}