Aligning multiple equation environments with cases

Question

I have some code that works but I wish to align the environments according to the descriptions. I've tried various combinations of align, equation and cases, but can't seem to find a functional solution.

\begin{equation}
  \textit{Initial conditions} \qquad \begin{cases}
  C\left(X,0\right) = S\left(X,0\right) = 0\\
  C\left(0,T\right) = 1
  \end{cases}
  \label{eq:dimensionless_initcond}
\end{equation}
\begin{equation}
  \textit{Continuous injection} \qquad  C\left(0,T\right) = 1 \label{eq:dimensionless_continuous}
\end{equation}
\begin{equation}
  \textit{Finite injection} \qquad C\left(0,T\right) = \begin{cases}
  1 \text{ for } 0 < T < T_0\\
  0 \text{ for } T_0 < T < \infty
  \end{cases}
  \label{eq:dimensionless_finite}
\end{equation}

Optimal case would be to have the environments such that both descriptions and equations are left aligned as seen in my badly done mspaint picture here:

Answer 1

My initial thought would be to place everything in an align environment as follows:

\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand{\mytext}[1]{\makebox[1.25in][l]{#1}\qquad}
\pagestyle{empty}
\begin{document}

\begin{align}
  \mytext{Initial conditions} 
  & \begin{cases}
      C\left(X,0\right) = S\left(X,0\right) = 0\\
      C\left(0,T\right) = 1
    \end{cases}
    \label{eq:dimensionless_initcond}
  \\[2ex]
  \mytext{Continuous injection} 
  &
    C\left(0,T\right) = 1 
    \label{eq:dimensionless_continuous}
  \\[2ex]
  \mytext{Finite injection} 
  &
  C\left(0,T\right) 
    = 
    \begin{cases}
      1 \text{ for } 0 < T < T_0\\
      0 \text{ for } T_0 < T < \infty
    \end{cases}
  \label{eq:dimensionless_finite}
\end{align}

\end{document}

Since the align environment wants to make the material in the first column right aligned, I create a box to wrap the text there \mytext which you can format as you want. It uses a \makebox whose syntax is:

\makebox[<width>][<alignment>]{<text>}

The <alignment> here can be left l, right r, or center which is the default.