As usual, let $\mathcal RL$ denote the ring of real-valued continuous functions on a completely regular frame $L$. Let $\beta L$ and  $\lambda L$ denote the  Stone-\v{C}ech compactification of $L$ and the Lindel\"of coreflection of $L$, respectively. There is a natural way of associating with each sublocale of $\beta L$ two ideals of $\mathcal RL$, motivated by a similar situation in $C(X)$. In~\cite{DS1}, the authors go one step further and associate with each sublocale  of $\lambda L$ an ideal of $\mathcal RL$ in a manner similar to one of the ways one does  it for sublocales of $\beta L$.  The intent in this paper is to augment~\cite{DS1} by considering two other coreflections; namely, the realcompact and the paracompact   coreflections.\\        We show that $\boldsymbol M$-ideals of $\mathcal RL$ indexed by sublocales of $\beta L$ are precisely the intersections of maximal ideals of  $\mathcal RL$. An $\boldsymbol{M}$-ideal of $\mathcal RL$ is \emph{grounded} in case it is of the form $\boldsymbol{M}_S$ for some sublocale $S$ of $L$. A similar definition is given for an  $\boldsymbol{O}$-ideal of $\mathcal RL$.  We characterise $\boldsymbol M$-ideals of $\mathcal RL$ indexed by spatial sublocales of $\beta L$, and $\boldsymbol O$-ideals of $\mathcal RL$ indexed by closed sublocales of $\beta L$ in terms of grounded maximal ideals of $\mathcal RL$.

This paper deals with the spatial behavior of solutions for a viscoelastic wave equations with nonlinear dissipative terms in a semiin , nite n-dimensional cylindrical domain. An alternative of Phragm, en-Lindel, of type theorems is obtained in the result. In the case of decay, an upper bound will be derived for the total energy by means of the boundary data. The main point of the contribution is the use of energy method.