- #1

latentcorpse

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\begin{document}

\begin{subequations}

\begin{equation}

U(\theta,t)=\beta \ln{t} + \gamma + \nu(\theta,t) t^{-\frac{1}{2}}+\kappa(\theta,t)

\end{equation}

where $\beta$ and $\gamma$ are constants, $\nu$ is a bounded solution of the wave equation $\nu''=\ddot{\nu}$ and the remainder, $\kappa$, obeys

\begin{align*}

| \kappa(\theta,t) | &\leqslant C_7 t^{-\frac{3}{2}} \\

| \partial_t \kappa(\theta,t)| &\leqslant C_8 t^{-\frac{3}{2}}

\end{align*}

and

\begin{equation}

A(\theta,t)= \begin{cases}

\alpha + \beta^2 \ln{t} & \quad \text{ if $\nu(\theta,t)=0 \forall \theta,t$} \\

\delta t + \epsilon(\theta,t) & \quad \text{ if $\nu(\theta,t) \neq 0$ for some $\theta$ and $t$}

\end{cases}

\end{equation}

\end{subequations}

\end{document}