In previous sections we looked at solutions defined for all $$x\in\mathbb{R}^n$$ and $$t\in\mathbb{R}^1$$. In this and in the following section we seek solutions $$u(x,t)$$ defined in a bounded domain $$\Omega\subset\mathbb{R}^n$$ and for all $$t\in\mathbb{R}^1$$ and which satisfy additional boundary conditions on $$\partial\Omega$$.