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%%
%% An UIT Edition example
%%
%% Example 01-00-3 on page 4.
%%
%% Copyright (C) 2010 Herbert Voss
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
%%
%% See http://www.latex-project.org/lppl.txt for details.
%%
%%
%% ====
% Show page(s) 1
%%
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{375.57637pt}
\setlength\parindent{0pt}
\setcounter{equation}{3}
\renewcommand\theequation{1.\arabic{equation}}
\StartShownPreambleCommands
\usepackage{amsmath,esint}
\newcommand\abs[1]{\left\lvert#1\right\rvert}
\newcommand*\diff{\mathop{}\!\mathrm{d}}
\StopShownPreambleCommands
\begin{document}
\setlength\jot{15pt}
\begin{align*}
\begin{split}\abs{I_1} &= \left\lvert \int_\Omega gRu\diff\Omega\right\rvert\\
& \le C_3\left[\int_\Omega\left(\int_{a}^x g(\xi,t)\diff\xi\right)^2\diff\Omega\right]^{1/2}
\times\left[\int_\Omega\left\{u^2_x+\frac{1}{k}
\left(\int_{a}^x cu_t\diff\xi\right)^2\right\}\diff\Omega\right]^{1/2}\\
& \le C_4\left\lvert \left\lvert f\left\lvert \widetilde{S}^{-1,0}_{a,-}W_2(\Omega,\Gamma_l)
\right\rvert\right\rvert\left\lvert \abs{u}\overset{\circ}\to W_2^{\widetilde{A}}
(\Omega;\Gamma_r,T)\right\rvert\right\rvert.
\end{split}\\
\begin{split}\abs{I_2} &= \left\lvert \int_{0}^T \psi(t)\left\{u(a,t)
-\int_{\gamma(t)}^a\frac{\diff\theta}{k(\theta,t)}
\int_{a}^\theta c(\xi)u_t(\xi,t)\diff\xi\right\}\diff t\right\rvert\\
& \le C_6\left\lvert \left\lvert f\int_\Omega\left\lvert \widetilde{S}^{-1,0}_{a,-}
W_2(\Omega,\Gamma_l)\right\rvert\right\rvert\left\lvert \abs{u}\overset{\circ}
\to W_2^{\widetilde{A}}(\Omega;\Gamma_r,T)\right\rvert\right\rvert.
\end{split}\tag{\theequation$'$}
\end{align*}
\end{document}
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