What is the difference between boundary conditions and initial conditions?
I have two condition. The first is a boundary condition
\begin{equation}
\theta (\mathbf{x},t)=k(\mathbf{x},t),\hspace{0.2cm}\mathbf{x} \in A, t>0
\end{equation}
And the second is the initial condition
\begin{equation}
\theta (\mathbf{x},0)=h(\mathbf{x}),\hspace{0.2cm}\mathbf{x} \in B, t=0
\end{equation}.
Why $t=0$ is not taken in boundary condition and in initial condition why not $t>0$?
Best Answer
The names themselves telling the meaning. Boundary conditions are those which depends on space while initial conditions are depends on time. So, in boundary condition space coordinate will be varied and in initial conditions time will be varied.